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Advanced Engineering Informatics 57 (2023) 102074
Available online 18 July 2023
1474-0346/© 2023 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Full length article
A Novel Integrative Design Framework Combining 4D Sketching, Geometry
Reconstruction, Micromechanics Material Modelling, and
Structural Analysis
S. Rasoulzadeh
a
,
*
,
1
, V. Senk
b
,
1
, M. K¨
onigsberger
b
, J. Reisinger
a
, I. Kovacic
a
, J. Füssl
b
,
M. Wimmer
c
a
Research Unit of Integrated Planning and Industrial Construction, Vienna University of Technology, Vienna, Austria
b
Research Unit of Structural Simulation and Timber Engineering, Vienna University of Technology, Vienna, Austria
c
Research Unit of Computer Graphics, Vienna University of Technology, Vienna, Austria
ARTICLE INFO
Keywords:
Early-design stage
Sketch-based interface
Sketch-based modelling
Machine learning
3D reconstruction
Material-informed
Micromechanics
Multiscale modelling
Biocomposite
Structural analysis
Finite element analysis
ABSTRACT
State-of-the-art workows within Architecture, Engineering, and Construction (AEC) are still caught in
sequential planning processes. Digital design tools in this domain often lack proper communication between
different stages of design and relevant domain knowledge. Furthermore, decisions made in the early stages of
design, where sketching is used to initiate, develop, and communicate ideas, heavily impact later stages,
resulting in the need for rapid feedback to the architectural designer so they can proceed with adequate
knowledge about design implications. Accordingly, this paper presents research on a novel integrative design
framework based on a recently developed 4D sketching interface, targeted for architectural design as a form-
nding tool coupled with three modules: (1) a Geometric Modelling module, which utilises Points2Surf as a
machine learning model for automatic surface mesh reconstruction from the point clouds produced by sketches,
(2) a Material Modelling module, which predicts the mechanical properties of biocomposites based on multiscale
micromechanics homogenisation techniques, and (3) a Structural Analysis module, which assesses the mechanical
performance of the meshed structure on the basis of the predicted material properties using nite element
simulations. The proposed framework is a step towards using material-informed design already in the early
stages of design.
1. Introduction
Architecture, Engineering, and Construction (AEC) shapes our built
environment, having a substantial environmental, cultural, and eco-
nomic inuence on society. However, among the least digitized in-
dustries, it is still caught in silo-thinking and sequential planning
processes, as experts from different disciplines must work together and
communicate throughout different stages of the design. Conventional
AEC workows typically involve a sequence of processes that are per-
formed consecutively, with each domain expert performing their
particular tasks (such as design, analysis and calculation) based on in-
formation and planning documentation from previous stages. While this
approach helps reducing the complexity of the problem, it often leads to
sub-optimal designs, as some important aspects may not be considered,
and it may not be possible to make changes effectively in later stages
[19]. In particular such sequential design process is error prone due to
information losses between the steps and causes increasing planning
costs and time due to long feedback loops. Further, it prevents creating
joint knowledge and design optimisation in the earliest design stages,
which are crucial for the latter building performance throughout the
lifecycle. Unfortunately, the current professional fee structures still do
not enhance integrated collaboration nor do these enhance additional
efforts needed for the design optimisation in the early design stages.
Thus, due to sequential planning practice, the ow of information ex-
change within current workows between the domain experts with
various domain knowledge is challenging, impeding optimised pro-
gression. A new approach to solve this problem is to closely connect
Architecture, Computer Science, Engineering, Material Science and
* Corressponding author.
E-mail addresses: shervin.rasoulzadeh@tuwien.ac.at (S. Rasoulzadeh), valentin.senk@tuwien.ac.at (V. Senk).
1
These authors contributed equally.
Contents lists available at ScienceDirect
Advanced Engineering Informatics
journal homepage: www.elsevier.com/locate/aei
https://doi.org/10.1016/j.aei.2023.102074
Received 15 January 2023; Received in revised form 12 April 2023; Accepted 22 June 2023
Advanced Engineering Informatics 57 (2023) 102074
2
Mathematics to develop innovative computational design tools [62],
combining implicit (e.g., aesthetical, cultural, or emotional) and explicit
(e.g., functional, environmental, economic) knowledge. An important
foundation for such tools would be the establishment of an integrative
design framework that provides rapid feedback already in the early
stages of design.
In this context, many critical decisions can occur when a design is in
its roughest form, namely a sketch [33]. Sketching is used to initiate,
develop, and communicate ideas while allowing the architectural
designer to easily tap into their intuition to ideate and explore the so-
lution space. In the early stages of design, sketching serves as a visual
thinking and architectural form-nding process for the designer and,
subsequently, as a visual reference for Computer-aided Design (CAD)
[11]. To create the 3D digital model, such an architectural sketch is
usually converted manually into a suitable geometric format by a
modelling expert, which can be time consuming and prone to mis-
interpretations regarding the designer’s original intent. For this
reason, recent advancements in sketch reconstruction methods [67,68,
63] offer a promising alternative for handling sketch inputs, as they not
only robustly reconstruct 3D models but also implicitly capture the
design intent. Furthermore, the derived 3D digital model enables further
communication with other downstream processes, such as structural
analysis, including the choice of adequate building materials,
Computer-aided Engineering (CAE) simulations [15], and
manufacturing. Additionally, structural analysis is an essential part of
the design. It veries the mechanical feasibility and safety of a structure
made of a particular material subjected to different loads. Regarding the
material, environmental concerns, particularly the high CO
2
emisions
associated with traditional construction materials such as concrete [42],
and rapidly emerging new production technologies such as 3D printing
force designers to often adapt or tailor their design to the intended
materials. Material-informed design strategies are thus increasingly
popular [10,49]. As an additional challenge, modern environmentally
friendly construction materials such as biocomposites, a polymer matrix
reinforced by natural bres, come in large varieties, given the different
bres and polymers that are usable in different qualities and quantities,
and given the different bre orientations and different bre lengths,
which all lead to substantially different mechanical material properties
[12]. These promising materials not only come in a very large variety
but also show a more complex mechanical behaviour than conventional
building materials. For this reason, it will become even more important
to implement fundamental material understanding in the early planning
phases. Therefore, multiscale material modelling approaches [35,34,27]
are essential to characterize the performance of such materials.
Building upon the above statements, this paper presents a framework
that aims at shifting the design paradigm away from a sequential process
towards an automated and integrative approach. Two main objectives
are dened: Firstly, concept design and digital modelling are bridged by
an automated translation of designed sketches into an appropriate ge-
ometry format. Secondly, the structural performance of the design is
quantied through quasi-immediate feedback from material modelling
and structural analysis. In other words, this innovative framework seeks
to integrate digital design, material modelling, and structural analysis.
This enables quick iterations throughout the design cycle, allows for
comprehensibly tracing the implications of changes in design and ma-
terial on the structural response, reveals optimisation potentials and
thus leads to structures of higher quality.
To achieve these objectives, the proposed integrative design frame-
work contains four modules: A 4D Sketching Interface [28], an architec-
tural form-nding tool simulating traditional sketching behaviour with
paper and pen allowing the sketch creation in 3D space through tablet
and stylus while capturing temporal data as a fourth dimension. A
Geometric Modelling module, translating the sketch to a volume mesh
based on a reconstructed surface mesh of the 3D sketch’s point cloud
[16]. Next, information on the mechanical material behaviour is ob-
tained from a Material Modelling module, relying on a recently developed
multiscale micromechanics model for natural bres and biocomposites
[27]. Finally, the volume mesh along with the material information is
processed using nite element simulations in the Structural Analysis
module, whereby feedback based on the mechanical performance of the
design is sent back to the sketching interface.
More details regarding the individual modules are presented in
Section 3, after discussing related works in the following section.
Finally, as a proof of concept, the efciency of the proposed framework
is demonstrated in Section 4 based on two sketched structures, a stage
wall in a theatre setting and a dome-like pavilion in resemblance to the
BUGA Wood Pavilion [9,1]. The paper is closed with conclusions (Sec-
tion 5) and an extensive outlook on future work (Section 6).
2. Related works
A wide range of studies have been targeting the early stages of
design, where sketching is used to communicate ideas. Within this
context, while some studies’ focus has been solely on developing
sketching interfaces, others have been attempting to introduce new
interaction setups to account for more accurate sketching and another
group addressed modelling and/or (material-informed) structural
analysis along with unique self-developed interfaces.
2.1. Sketching interfaces
The sketches created with conventional sketching interfaces mainly
fall into the two categories of 2D and 3D. Some sketching interfaces
allow the creation of both 2D and 3D sketches via the stylus or mouse-
based devices. With such interfaces, 2D sketches form by positional in-
formation in 2D coordinate systems, while 3D sketches often happen via
mapping 2D stroke coordinates to the 3D drawing canvases [69]. On the
other hand, A variety of recent sketching interfaces facilitate direct
sketching in 3D using augmented or virtual reality gear and input de-
vices. Quill and TiltBrush are two commercial examples of such in-
terfaces that directly map the strokes points positions to the designer’s
movement with a freehand sketching technique. These interfaces do not
perform strokes beautication and thus, output a set of disconnected
rough strokes. GravitySketch is another Virtual Reality (VR) shape cre-
ation targeting industrial design. Within this interface, designers can
create freeform 3D strokes without an accompanying beautication al-
gorithm applied to them. However, as pointed out by Multiplanes [32],
one problem with freehand sketching systems is that they are less ac-
curate compared to 2D and 3D geometric sketches. As a step towards
overcoming such challenges with freehand 3D sketching, [3] worked on
an interface named SymbiosisSketch, a hybrid sketching system which
combines 3D mid-air and 2D sketching on a surface, enabling the cre-
ation of a detailed 3D design. The designer could create planar or curved
canvases and use a tablet for sketching onto them. Within this interface,
sketches are created in situ, in the context of physical objects in the
scene. Similarly, VRSketchin [13] proposes another VR sketching
interface that uses a 6DoF-tracked stylus and a 6DoF-tracked tablet as
input devices combining unconstrained 3D mid-air with constrained 2D
surface-based sketching. A further recently researched and developed
sketching interface named ScaffoldSketch [70] presented an in-air
design two-staged approach sketching interface inspired by 2D design
sketching practice.
2.2. Sketch beautication
Sketch beautication and simplication methods generally rene
oversketched 2D/3D strokes by tting single curves to groups that are
perceived visually as such individual curves. Various developed
methods arise from the need for geometrically constrained diagrams or
drawings from rough sketches. [43] proposed a method that parses
digitally-created 2D sketches into beautied curve segments. They use a
supervised learning algorithm based on three geometric features
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
3
extracted from each stroke pair. [54] introduced a sketch simplication
model leveraging a fully convolutional neural network and a dataset of
pairs of rough and simplied 2D drawings for training their simplica-
tion model. Multiplanes [32] is a VR sketching interface that allows
recognition of the type of stroke based upon the geometric relationship
between controller position and previous strokes, leading to automated
beautication of strokes that are projected onto a designer-generated
planar surface. StrokeAggregator [30] improves considerably upon
state-of-the-art by leveraging principles derived from human perception
research and artistic practices for clustering 2D strokes and tting
polylines into groups dening aggregate curves. Inspired by 2D sketch
beautication methods, CASSIE [68] proposed a 3D beautication
process that allows connecting each new 3D stroke to as many nearby
curves as possible while staying close to the original trajectory, with the
aim of forming a curve network enabling surface inference.
2.3. 3D sketching interfaces coupled with modelling
On the other hand, regarding 3D sketching interfaces coupled with
modelling, [67] presents the prototype of a 3D sketching interface to
enhance the design exploration in the early stages. The prototype uses
ML enabling the translation of the sketch into an intermediate descrip-
tion followed by a reconstruction function that translates this descrip-
tion into a 3D form. The reconstruction function and a set of libraries
containing various geometric elements enable the designer to rene the
solution space and produce different outputs from the same sketch
without retraining the model. [51] introduced SurfaceBrush, a surfacing
method which converts coarse VR drawings of varying widths and
ribbon-like 3D brush strokes into user-intended manifold free-form 3D
surfaces. CASSIE [68] is another conceptual modelling system which
leverages freehand mid-air sketching coupled with a 3D optimisation
framework performing automatic surface neatening, resulting in
well-connected 3D curve networks. These curve networks are further
surfaced, making them amenable to presentation, structural analysis,
and manufacturing. In their late work [63], the same authors proposed a
new method to transform unstructured 3D sketches drawn with
immersive 3D drawing and sketching interfaces into piecewise smooth
surfaces that preserve sketched geometric features. Aligned with the
way humans imagine such sketches, starting with an initial proxy sur-
face, they iteratively segment and optimise the surface patches to t
surrounding strokes.
2.4. Sketching interfaces integrating structural analysis
Additionally, a few other sketching interfaces integrating structural
analysis have been introduced. However, they work within 2D instead of
3D sketches and are mainly developed for educational purposes. The
FEAsy [38] is a sketch-based environment for structural analysis in the
early stages of design in which the designer can transform, simulate, and
analyse their nite element models through freehand sketching within
this environment. The tool is coupled with a beautication module
responsible for simplication and representation in a more meaningful
way prior to the Finite Element Analysis (FEA). STRAT [47] is another
tool developed specically for solving truss problems. Using the free-
hand sketch of the truss, this tool allows the designer to determine un-
known forces in it with the aid of a sketch recognition system. SMATS
[36] is a domain-specic 2D sketch method for the analysis and
modelling of the form and structures of trusses concurrently. Within its
environment, a structure is sketched, subjected to loads, a structural
analysis is performed, and the results of the various sketched scenarios
can be visualised.
2.5. Articial intelligence for structural design
A handful of studies address supporting the architectural designer in
the early stages of design through structural recommendations and
performance simulations relying on machine learning/deep learning
models but do not lie precisely in one of the categories above. [2] trained
a Convolutional Neural Network (CNN), which iteratively generates
structural design solutions for the sketches of the plans accompanied by
real-time guidance before formalisation into CAD software. Other works
used ML as surrogate models to speed-up simulations that are time-
consuming to be employed in the early stages of design. [39] uses a
CNN for predicting stress elds in 2D linear elastic cantilevered struc-
tures. Successively, the same author proposed a new data-driven to-
pology optimisation titled TopologyGAN [40], which uses a conditional
Generative Adversarial Network (cGAN) that uses various physical elds
computed on the original, unoptimised material domain as inputs and
outputs the optimised topology of the solid structure. [23] achieved a
fast mechanical analysis by introducing a new network architecture
called StressGAN for predicting 2D von Mises stress distributions in solid
structures.
2.6. Material-Informed structural design
Lastly, Material-informed structural optimisation algorithms for
anisotropic (bre-reinforced) materials have existed for quite a while
[50], e.g., an algorithm like the Computer-aided Internal Optimisation
(CAIO) optimises macroscopic material behaviour by aligning bres to
the principal normal stress trajectories. Recent developments in this
[60,59] and related elds, like the Free Material Optimisation-approach
(FMO) [55], combine topology and material optimisation. [37] present a
customized computational design-to-3D-printing framework for form-
nding of compression-only structures combined with a material dis-
tribution optimisation method.
Nevertheless, it must be pointed out that although various studies in
numerous elds have been done, to the best of the authors’ knowledge,
there is no research addressing the harmonious integration of material-
informed structural analysis of early stages of design sketches in a single
unied framework.
3. Integrative design framework
3.1. Overview
The proposed integrative design framework, depicted in Fig. 1, starts
with the designer drawing a sketch in the (a) Sketching Interface. The
sketch is built up by 3D strokes and associated recorded data, which are
exported and sent to the (b) Geometric Modelling module for recon-
struction. The 3D strokes of the sketch are rst converted into a 3D point
cloud making use of geometry and stylues-related properties in a pre-
processing step. Subsequently, the shape inference step outputs the
reconstructed surface mesh of the original sketch. Finally, the surface
mesh is converted to a volume mesh in a post-processing step to create
an appropriate input format for the Structural Analysis module.
In addition to the geometry features of the design, the designer se-
lects adequate material classes for the load-bearing elements of the
structure from a database that is based on (c) multiscale material
modelling predictions. In more detail, the designer can choose between
different material classes (such as concrete, wood, steel, biocomposites,
etc.) as well as between different material specications within the
selected class and can then assign the materials to the structure. Given
the focus on biocomposites, the type of bre, the type of polymer, as well
as bre distribution/orientation or bre–matrix interface parameters
can be chosen or left at their default setting. If a new material is dened,
the Material Modelling module computes the mechanical material
properties required for the structural analysis based on the material
composition.
The material properties as well as the volume mesh are then used
within the (d) Structural Analysis module to assess the performance of
the designed structure. To this end, the designer or engineer adds
appropriate boundary conditions to the structure, including loads and
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
4
bearings. Finite element calculations are performed, and the resulting
stress and displacement elds are visualised in the sketching applica-
tion. Visual aids, such as colour maps of intact structural elements and
parts which exhibit stresses beyond their limits, assist the designer.
Given the quasi-immediate feedback regarding the mechanical perfor-
mance of the design, the designer can now iteratively optimise the
structure in two ways, as indicated by two feedback loops in Fig. 1: The
designer can optimize the geometry of the structure, e.g., by adding
additional supports, modifying the span length, or improving the shape
towards mechanically efcient structural elements such as arches. As an
alternative, or in addition, the designer can optimise the material used
for the whole structure or for some specic elements, e.g., by selecting
high-performance composites for highly stressed elements or by better
aligning the bres in the direction of the principal stresses.
In the subsequent sub-sections, the four integral parts, the 4D
sketching interface, the geometric modelling, the material modelling,
and the structural analysis, are discussed.
3.2. 4D sketching interface
The framework is based on a 4D sketching interface targeted for
architectural design [28]. It utilises a tablet (iPad) and a stylus (Apple
Pencil) as its primary drawing medium. The interface enables the cre-
ation of 4D sketches by employing 3D drawing canvases and projecting
drawn 2D stroke coordinates onto them. Temporal data of all strokes are
continuously captured throughout the drawing process, which provides
a fourth dimension, namely time, to the sketch and its constituent
strokes. This way, valuable information on design intents is recorded
and may be further used in sketch analysis pipelines.
The interface is composed of a ground plane within its environment
and offers a choice of various geometric primitives as drawing canvases,
including plane, cube, sphere, and cylinder, which can be placed
arbitrarily (positioned, rotated, and scaled) in the scene. The designer
also has control over the camera view position and rotation. Once the
canvas and the camera view are in the designer’s desired trans-
formation, the designer could lock the canvas transform and start
drawing on the canvas from their viewpoint. In this setting, as the
designer starts drawing strokes on the tablet’s surface, the ray origi-
nating from the camera view is intersected with the canvas and the
resulting 3D point is stored for the continuation of the stroke polyline.
The sequence of such points forms a 3D stroke, see Fig. 2. The brush
strokes are rendered as ruled surfaces or triangle strips of user-specied
colour and width centred around the captured stroke polyline positions
lying on the canvas.
Furthermore, the designer can switch between sketch mode and
select mode. Via select mode, previously drawn strokes can be selected
at any stage of drawing to assign materials from the database, such as
concrete, steel or biocomposites. In addition, the designer is able to
translate, rotate, or delete the selection and is provided with undo and
redo options (given the temporal information) as well as clearance of the
scene for starting over. It is noteworthy that the designer is not limited to
use just one single canvas, and the overall sketch can be drawn using
multiple canvases of the same or different types in combination,
enabling the design of complex objects.
Throughout the drawing process, two levels of information (geom-
etry and stylus-related) are recorded, stroke-level and stroke-point-level;
Each stroke is attributed with properties such as inkWidth, inkColour,
cameraViewPosition, cameraViewRotation, canvasId, and canvasTrans-
form. Also, as for stroke-point-level attributes, properties such as time-
stamp, position, normal, tilt, twist, pressure, and materialInfo are recorded.
Once the sketching is nished, all this info can be exported into a single
JSON le to be further used for sketch analysis. Moreover, besides the
JSON le, the designer can export the whole sketch to a single OBJ le
comprising drawn strokes as triangle strips. Fig. 2 depicts four
Fig. 1. Overview of the proposed integrative design framework.
Fig. 2. Four sample conceptual sketches. (a) Drawn using plane canvas. (b) Drawn using a cylinder as canvas. (c) and (d) are both drawn using a sphere canvas.
Sketches drawn by Ingrid Erb.
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
5
conceptual sketches of stage walls in a theatre setting. Fig. 3 shows four
additional sketches, which take four actually built structures as a visual
reference. All the sketch images are rendered using Polyscope [53].
3.3. Geometric modelling
Once the sketching is nished, the sketch comprising designer-drawn
strokes must be converted into a suitable geometric format that makes it
usable for other downstream processes. Recently, there has been a lot of
research and development on 3D mesh reconstruction from sketches. As
described in the Related Works section, each of the developed 3D
sketching interfaces comes with its own set of recorded data or own
sketching rules, requiring the development of a specic reconstruction
algorithm dealing with its specic data type. The same argument applies
to our sketching interface, particularly when considering the timestamp
attribute recorded as the fourth dimension. However, recent de-
velopments in machine-learning methods for surface reconstruction
from point clouds [16,45] suggest that converting the sketch into a point
cloud may serve as a viable starting point. By relying on these algorithms
and excluding the timestamp, we focus solely on utilizing point co-
ordinates for the reconstruction process treating this as an initial
approach. Following this path, the points sampled as 3D stroke polyline
positions, or a dense set of points sampled along the stroke triangle
strips, could be an option for conversion of the 3D strokes of the sketch
into a point cloud.
Several methods have been developed to reconstruct surfaces from
point clouds. They mainly fall into two categories: non-data-driven and
data-driven. Within non-data-driven approaches, Poisson surface recon-
struction [71] is the current standard. While it is a general approach, it
fails to handle partial or noisy input point clouds, which could be the
case due to the nature of sketching and the way point clouds are
generated from sketches within the sketching interface. On the other
hand, recently, several methods have been proposed which learn a prior
of typical surface shapes of a large dataset. Generally, these methods do
not perform well on unseen objects. However, a recent algorithm,
Points2Surf [16], in contrast to other learning-based surface recon-
struction algorithms, is patch based and independent from classes and
leads to a better generalisation ability on unseen inputs compared to
other surface reconstruction algorithms such as DeepSDF [45], AtlasNet
[58], and SPR [72], making it a reasonable choice to start with.
Treating the strokes as triangle strips and exploiting the stored
canvas normal vectors at the strokes’ polyline positions, automated pre-
and post-processing steps are employed. These steps, independent of the
sketched structure, prepare the input point cloud for the Points2Surf
model and rene and convert surface meshes before transferring them to
the Structural Analysis module.
3.3.1. Pre-Processing
To be able to utilise the Points2Surf model, the sketch must be
converted into a point cloud. One approach could be just relying on the
contact points that are originally recorded via ray casting at every frame
at which the Update function of the Unity Engine gets called. A 3D point
cloud of the whole sketch can then be obtained by merging the indi-
vidual 3D points of all strokes’ polyline positions into one unied point
cloud. However, relying on this approach may impose two difculties
for Points2Surf; rstly, it could lead to a point cloud of varying densities
throughout different regions as the drawing speed varies throughout the
sketching and accordingly the number of sampled points. Secondly,
since Points2Surf is trained on solid objects with an implicit front and
back, it only performs well on point clouds of solid objects.
If only individual recorded points of stroke polyline positions are
considered, it could result in the failure of the algorithm, either because
of low point density or due to non-solidness of the sketched geometry,
see Fig. 4.
Our observations reveal that designers communicate their envi-
sioned geometry by drawing a dense set of strokes that cover the surface
of their intended geometry. Relying on this, to overcome the problems
mentioned above, we devised another method by creating a virtual point
cloud through ray casting using the triangle strips of each stroke and
canvas normal vectors at stroke points recorded in the JSON le. Firstly,
the normal vectors at each stroke points are extracted and averaged,
resulting in a single normal vector associated with the stroke. Secondly,
each stroke’s corresponding triangle strip is extruded along the normal
direction with the magnitude of stroke ink width. Afterwards, having the
sketch centred at the origin (0.0, 0.0, 0.0), we cast rays using eight
different pinhole cameras surrounding the sketch, each looking at the
centre with the resolution of 720 ×480 and 90 degrees horizontal eld
of view (See Fig. 5). Using casted rays, we record the XYZ coordinates of
the intersection points with the extruded triangle strips resulting in a
very dense virtual point cloud of the sketch, see Fig. 5.
In such a manner, the two difculties mentioned earlier are
compensated: rstly, the solidness of each stroke turns the whole sketch
into a solid and, accordingly, matches to the type of point clouds that
Points2Surf is trained on. Secondly, since point clouds are obtained from
triangle strips, setting the resolution of the pinhole camera can lead to a
very dense point cloud independent of drawing speed and sampled
points within Unity’s update frame rate. Fig. 6 depicts the point cloud of
the same sketch as the one in Fig. 6 obtained with the newly devised
method.
Prior to feeding point clouds to Points2Surf, other than centring at
the origin, they are scaled uniformly to t within the unit cube.
3.3.2. Shape inference using Points2Surf
Points2Surf [16] is a neural network model for reconstructing a 3D
Fig. 3. Each of the sketches has been drawn using actual built structures as visual reference. (a) [9]. (b) [57]. (c) [46]. (d) [14].
Fig. 4. Point cloud creation from the sketch using the points sampled originally
by Unity along each stroke. (a) The original sketch, and (b) the sampled
point cloud.
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
6
surface mesh S from a 3D point cloud P= {p1,p2, ..., pN}. The authors
used the zero set of the Signed Distance function (SDF) as a represen-
tation of surfaces for training the neural network.
S=L0(fS) = x∈R3|fS(x) = 0(1)
The approach taken in Points2Surf consists in feeding the point cloud
to a neural network with an encoder-decoder architecture, generating a
latent vector and approximating the SDF through the decoder:
fS(x) ≈
fP(x) = s(z),with z =e(P)(2)
where z is the latent vector obtained through the encoder e from the
point cloud P, and s is the decoder conditioned on the latent vector z.
However, it is argued that encoding a surface with one single latent
vector reduces the network’s accuracy and generalisation ability.
Consequently, the authors proposed factorising the SDF into two pa-
rameters: absolute distance fd
S and sign of the distance fs
S, where each of
them is estimated through separate encoders ed and es, while sharing the
two vectors in a single decoder, resulting in the following formulation:
fd
P(x),
fs
P(x)=szd,zs,with zd=edpdand zs
x=es(ps),(3)
where s is the decoder containing the zd and zs as its inputs, outputting
the distance
fd and the sign of the distance
fs. Afterwards, the surface S
can be reconstructed by applying Marching Cubes [31] to the predicted
SDF
fd*
fs.
The network architecture used for encoders ed and es is the same as
PointNet [48], where a feature representation for each point is
computed through a 5-layer Multi-layer Perceptron (MLP) neural
network. The decoder s consists of a 4-layer MLP that takes as input the
concatenated feature vectors zd and zs and outputs the two SDF factors.
Assuming the ground-truth surfaces are available during the training,
the above network is trained in an end-to-end manner, regressing the
distance and classifying the sign as positive or negative based on the
interiority and exteriority, respectively. Two separate loss functions are
used for the distance and the sign of the distance for the training pro-
cedure. Firstly, L2-based regression is used for the distance:
Ld(x,P,S)= |tanh
fd(x)
−tanh(|d(x,S) | )|2
2(4)
where d(x,S)is the ground-truth distance between the query point x and
surface S. Secondly, for sign of the distance classication, the binary
cross-entropy loss H is used as follows:
Ls(x,P,S) = H
σ
fs(x),[fS(x)>0](5)
where
σ
is the logistic function converting the sign logits to probabilities,
and fs(x)>0is equal to 1 when x resides in the exterior of the surface
and is equal to 0 otherwise. Altogether, the network is optimised with
the following loss function comprising the summation over these two
losses for all shapes and their corresponding query points of the training
set:
.
(P,S)∈S.
x∈XS
Ld(x,P,S) + Ls(x,P,S)(6)
In the original paper, ABC dataset [24] is chosen to train the
network. This dataset includes a collection of one million CAD models.
The authors picked 4950 clean watertight meshes for training and 100
meshes for validation and test sets.
Ultimately, for the inference on the point clouds of the sketches
drawn in the developed sketching application, we have chosen and
utilized their best pre-trained model based on the ablation results
trained for 250 epochs.
Depicted in Fig. 7 and Fig. 8, the reconstructed surface meshes of the
two sets of sketches shown in Figs. 2 and 3 can be seen.
3.3.3. Post-Processing
To translate the obtained surface mesh via Points2Surf into a format
suitable for structural analysis, several post-processing steps are neces-
sary. The reconstructed surface mesh may not be smooth enough and
may contain noise over its entirety and be rugged. To remove the noise,
Laplacian smoothing [61] is employed. After smoothing, it is crucial to
verify the watertightness of the surface mesh as it is a necessity for nite
element simulations. To this end, the approach introduced in the Man-
ifoldPlus method [22] is adopted to convert the reconstructed surface
mesh into a watertight one. ManifoldPlus extracts watertight manifolds
from surface meshes using the exterior faces between the occupied and
the empty voxels and a projection-based optimisation method. Subse-
quently, the reconstructed surface mesh is prepared for the application
of suitable boundary conditions required for the structural analysis. To
that effect, it is considered that the ground plane that exists in the
sketching application is the surface where boundary conditions are
prescribed. Therefore, the reconstructed surface mesh is automatically
sliced along the ground plane and subsequently capped.
Finally, the smoothed, watertight surface mesh with a planar bottom
is translated into an analysis-ready volume mesh using the TetWild [21]
engine, a quite robust engine that does not require any user interaction.
The quality of the resulting volume mesh is a direct function of the target
Fig. 5. 8 Pinhole cameras used for creating a virtual point cloud of a sketch
using ray casting. All the sketch’s constituent triangle strips are extruded by the
amount of strokes ink width.
Fig. 6. Virtual point cloud creation from sketch. (a) original sketch and (b) the
obtained point cloud through ray casting by pinhole camera. The point cloud on
the right is much denser while capturing the solidness of the sketch compared
to the one in Fig. 5.
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
7
mesh size, controllable by a tolerance parameter denoting how much
deviation from the initial surface mesh is permitted. Fig. 9 shows the
results of the processes involved in post-processing on a sample recon-
structed surface mesh.
3.4. Material modelling
A method called continuum micromechanics homogenisation is used
to predict the stiffness and strength of the materials used for structural
analysis based on their microstructure. This paper focuses on bio-
composites, a “green” composite material made of a biodegradable
matrix reinforced with natural bres, which are an increasingly popular
alternative to conventional building materials in the construction sector
[29]. Similar homogenisation tools have been successfully developed for
other building materials, including cementitious materials such as
concrete [26,25] and clay bricks [7,8] and can be integrated into the
workow. The variety of biocomposites is not only a consequence of the
choice of matrix and bre type, their dosage, and the potential use of a
coupling agent, but also arises from the composite production, which, e.
g., results in a certain alignment of bres in a 3D printer. Micro-
mechanics approaches, such as the one presented herein, are particu-
larly suitable to capture these variations. Moreover, continuum
micromechanics approaches provide an almost immediate result with
very little computational effort, and therefore represent the ideal com-
plement for material modelling in an architecture-focused sketching
application, where computational immediacy is of utmost importance.
The biocomposites for which the material modelling tool is set up are
characterized by a Representative Volume Element (RVE) with a char-
acteristic length of several centimetres, which is well below the scale of
the structure. It consists of three material phases: a homogeneous ma-
trix, embedded bres modelled as prolate spheroids with specic
orientation distribution, and spherical macropores, see Fig. 10. The
bres themselves exhibit a heterogeneous microstructure, and these
heterogeneities are resolved at smaller scales of observations, as
explained next.
On the one hand, the mechanical properties of natural bres vary
drastically, both among different species but also within a single species.
On the other hand, all natural bres exhibit a common microstructural
ngerprint, only the relative amounts of the constituents (mainly cel-
lulose and lignin) and their geometric arrangement change and entail
the observed differences in mechanical properties. This is why micro-
mechanics homogenisation is also used to predict the bre properties
themselves, based on the bre microstructure and the well-known me-
chanical properties of the constituents, leading to a recently developed
and validated multi-scale material model [27]. In more detail, the
technical bres used for biocomposite production are considered as bre
bundles. The bundles consist of a continuous matrix phase with
embedded lumen. We herein follow earlier micromechanics modelling
frameworks of wood [4] and consider cell walls in between the lumen to
consist of a matrix phase, labelled “polymer network”, where hemicel-
lulose, lignin and pectin are intermixed with nanopores. The cellulose
itself is considered as parallel microbrils (modelled as innitely long
cylinders), whose orientations are different than the orientation of the
bre. The difference is quantied by the microbril angle θ, a parameter
well known for its crucial inuence on the longitudinal bre properties
[18]. Finally, the cellulose microbrils are resolved at the nanoscale and
are considered to be a mix of an amorphous part and a crystalline part
with cylindrical shape and parallel arrangement.
The envisioned microstructure is used to predict elastic stiffnesses
and elastic limits, which enter the structural analysis tool, as discussed
next. The properties are “upscaled” from the nanoscale to the macro-
scale using micromechanics homogenisation by applying the self-
consistent scheme [20] for the RVE labelled “polymer network”, and
the Mori-Tanaka scheme [6] for all other RVEs. In more detail, the
Fig. 7. Inferred shapes of 4 conceptual sketches shown Fig. 2.
Fig. 8. Inferred shapes of 4 other sketches shown in Fig. 3.
Fig. 9. The reconstructed surface and volume mesh of the sketch from Fig. 7 (b). (a) Depicting perspective view of the triangular surface mesh, (b) showing planarity
at the bottom, and (c) the tetrahedral volume mesh generated by the TetWild Engine.
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
8
homogenized stiffness tensor Chom of an RVE with n material phases
reads as
Chom =
n
i=1
fiCi:Ai(6)
Where the fi denote the bre-specic phase volume fractions and are
tabulated for most natural bres, see e.g., [12],Ci are the phase stiffness
tensors, which are intrinsic for all bres and obtained, e.g., for cellulose
from atomistic modelling [56]. Moreover, Ai is the phase strain con-
centration tensor, which is a function of the phase shape and interaction
and results from Eshelby’s matrix inclusion problems [17], see, e.g. [64]
for more details. Step-wise stiffness upscaling by applying the homog-
enisation rule (6) consecutively for all RVEs nally leads to the sought
macroscopic stiffness of the biocomposite, which will be used in the
structural analysis tool.
As for predicting the elastic limit, two modes of failure are consid-
ered: tensile failure of the [52] crystalline cellulose at the nanoscale, and
von Mises-type failure of the matrix material at the biocomposite scale.
The macrostresses applied to the biocomposite RVE, Σ, are rst down-
scaled to the respective mean phase stresses
σ
i, using elastic stress
concentration relations reading as
σ
i=Bi:Σ, with Bi denoting the
stress concentration tensor, which is, by analogy to the strain concen-
tration tensor Ai introduced in Eq. (6), a function of the phase shape and
phase interaction. Failure is then initiated either if the downscaled
tensile stress of the crystalline cellulose exceeds the cellulose’s tensile
strength obtained from small-scale testing [52] available in the litera-
ture, or if the downscaled stresses of the biocomposite matrix lead to von
Mises-type failure, whereby the matrix’ von Mises strength is back-
calculated from macroscopic tensile strength tests on pure matrix
specimen, see e.g. [41,44].
To provide the designer with some pre-computed materials from
which they can choose, a material database for plant ber-reinforced
biocomposites is created, containing composites made from typical
plant bers and typical polymers, with typical mix designs. This pre-
calculation enables even quicker feedback for typical use cases.
3.5. Structural analysis
The nite element (FE) method is used to analyse and assess the
mechanical performance of the sketched structures. Geometrical fea-
tures of the structures are well dened by the post-processed volume
mesh obtained from the sketch (Section 3.2). The required mechanical
behaviour of a wide range of different biocomposite materials results
from the multiscale material model (Section 3.3). In addition to geom-
etry and material behaviour, boundary conditions and external loads are
required together with the selection of an appropriate FE solution
strategy, as discussed next.
The FE analysis is limited to linear elastic material models, given the
requirement of virtually real-time structural feedback for the designer in
the early design stage. First-order linear tetrahedral elements are used.
In order to test the consistency and functionality of the proposed
framework, at the moment, the calculations are performed within the
commercial FE-software ABAQUS. Therefore, the 3D mesh is imported,
loads and boundary conditions are dened, and the proper material
behaviour is allocated to the corresponding structural elements. In the
future, this process will be made smoother by adding the possibility to
dene loads and boundary conditions in the sketching tool, and by
developing an interface to link the FE model with an open-source FE
solver.
The computable output variables involve, among others, the 3D
nodal displacements as well as 3D stress- and strain elds of the struc-
ture. Graphical illustrations help the designer to rapidly assess the me-
chanical performance of the sketched structure. If certain displacements
are particularly large, or stresses exceed the material strength, the
designer can immediately react and can counteract on two fronts, either
by changing the structure – e.g., by changing the geometry or by adding
additional supports – or by selecting a stronger and stiffer material – e.g.,
by adding more bres to the biocomposite. The envisioned material-
informed design process is illustrated by two examples which act as a
Proof-of-Concept of the proposed workow.
4. Proof of concept
In the following we demonstrate two conceivable feedback loops for
a material-informed design process. Two of the sketched structures
shown in Fig. 2(c) and 3(a) were selected for this, as they represent two
different design intents. Use Case 1 is a curved wall intended to be used
in a theatre stage design scenario. The structure should be lightweight
and should visibly deform at both ends when an actor is hanging from
the top ends of the wall, supported by ropes. Use Case 2 is a larger
structure, resembling a dome-like pavilion similar in scale and design to
the BUGA Wood Pavilion built at the National Horticultural Show 2019
in Heilbrunn [5]. The structure should withstand all expected loads,
without breaking or without exceeding the stress limits. The demon-
strations therefore focus on the displacements for Use Case 1, and on the
internal stresses for Use Case 2. The two examples presented in this
section are deliberately simple structures to underline the workow in
the novel design framework. The approach can, however, straightfor-
wardly be extended to more complex structures including large build-
ings or even bridges. We note that the material-informed feedback loop
examined here is particularly important when dealing with complex
material behaviour, such as in the case of biocomposites.
4.1. Use Case 1: Curved wall in a theatre stage-design scenario
In this section we delve deeper into the design considerations and
analysis requirements for Use Case 1, a curved wall in a theatre stage-
design scenario.
In between the two upper corners of this wall, a cable is mounted,
which supports a person weighing roughly 100 kg. Therefore, a vertical
Fig. 10. Multiscale material model of biocomposites.
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
9
force F of 1 kN was applied, see Fig. 11(a1). The wall is supported at the
bottom plane. The dimensions L, H
1
, H
2
, B, and an assumption of the
angles
α
1
and
α
2
of the sagging cable under load are given in Table 1. In
addition to the applied force F, the deadweight of the structure, as a
function of the material density, is considered.
Given the focus on plant bre-reinforced composites, the designer
can choose from a range of diverse biocomposites with varying bre
content and bre orientation distributions. As for this example, a Flax-
Polypropylene (PP) composite is targeted, which is one of the most
common biocomposites and extensively described in the literature, see,
e.g., [41,44,65]. As for the initial design, 10 vol-% of typical ax bres
with properties obtained by homogenisation according to [27] are
considered to be randomly oriented and perfectly bonded to the PP
matrix, which also contains 50 vol-% of pores to achieve a lightweight
structure. The multiscale micromechanics model then provides the
isotropic mechanical behaviour, as specied in Table 1.
4.2. Use case 2: Permanent pavilion structure
Just as in the former example, a biocomposite material with
randomly distributed bre-orientation and, thus, in good approxima-
tion, isotropic material behaviour is considered. Further details on the
Kenaf-polylactic acid (PLA) biocomposite in this example and its me-
chanical properties are listed in Table 1. For this pavilion, only the load
case “deadweight” is studied, and “xed” boundary conditions are
placed on the nodes on its three basepoints.
4.3. Initial Design: Structural feedback
Fig. 11(b1) and (b2) show the structural feedback for both initial
designs under loading. For the theatre stage wall, we focus on the
displacement [Fig. 11(b1)]. The dashed lines indicate the free edges of
the undeformed structure, whereas for the deformed conguration, also
a heat map and a legend are added to highlight the zones with large
deections. The largest displacements are naturally at the top corners,
where the cables are mounted, and the maximum displacement amounts
to u
max,0
=32 cm, which is substantially more than what is tolerated by
the designer. As for the pavilion, in turn, the von Mises stresses are
visualised [Fig. 11(b2)] – a common stress quantity indicating failure for
ductile materials – with maxima of more than 100 MPa at the dark red
areas, which are way beyond the strength (maximum bearable von Mises
stresses) of the isotropic biocomposite, which amount to
σ
ult =54 MPa
according to the micromechanics model. In addition, the maximum
displacement of this initial conguration is 34 cm.
4.4. 1st Iteration: Enhancing structural feedback by optimising the
material
The material-informed structural analysis reveals inadequate initial
design requirements (e.g., geometric characteristics, material proper-
ties) for both sketched cases. The designer or the engineer now has
several avenues for improving the structural feedback, e.g., changing the
dimensions of the structure, adding supports, etc. We herein take a
closer look at material-informed optimisation strategies. One might
select other materials like concrete, steel, or timber, or iterate on the mix
design of the biocomposite. In our use case, we aim at changing the bre
content and bre orientation distribution such that the structural per-
formance improves, as discussed next.
We start with optimising Use Case 1, the theatre stage wall. In Fig. 11
(c1), regions are highlighted that exhibit high compressive and tensile
stresses according to the chosen loading-scenario. Reinforcing this sec-
tion with more bres (leading to a bre content of 40 %) at the expense
of pores should result in an improved performance. The implemented
multiscale material model provides, quasi immediately, a material with
improved macroscopic stiffness (E-modulus, Poisson’s ratio), as listed in
Table 1. Redoing the structural analysis with the updated stiffness values
in turn improves the structural performance, see Fig. 11(d1). The
maximum displacement value u
max,1
is now only 12 cm, and thus
roughly only one third of the initial design.
In Use Case 2, the dome-like pavilion structure, compressive stresses
dominate. This is why we aim at improving the performance by aligning
the plant bres with the direction of the principal stresses, as illustrated
in Fig. 11(c2). The resulting transversely isotropic material provides a
high stiffness and strength in the bre direction: the longitudinal
modulus increases from 5.12 to 29.0 GPa, the uniaxial compressive
strength almost triples to
σ
ult =149.0 MPa. Fig. 11(d2) shows the min-
imal (compressive) principal stresses, which are also aligned with the
bre direction. The stresses are consistently smaller than the compres-
sive strength. The global displacements of the optimised pavilion reduce
to one third compared to the original structure, with a maximum
displacement value of 11 cm.
This iterative process can be repeated multiple times for even better
results. The designer or engineer can optimise the material parameters
or redesign the geometry to explore the full potential of this framework
to achieve the desired structural performance.
5. Conclusion
A novel integrative design framework for architectural structures is
proposed, integrating architectural sketching, geometric modelling,
structural analysis, and material modelling. This framework is specif-
ically tailored to early stages of design, where ideation and exploration
still allow for considerable optimisations of the design. A cohesive and
efcient design process is established that overcomes the limitations of
the traditional sequential design workow. The two studied use cases
underline that the proposed framework meets the two main objectives:
•The automated transfer of the digitally designed sketches into an
appropriate geometry format for structural analysis is achieved by
linking a series of state-of-the-art algorithms, involving a ray-casting-
technique using pinhole cameras to generate virtual point clouds
from stroke-based 3D sketches, a pre-trained machine-learning al-
gorithm to reconstruct surface meshes (Points2Surf model), and an
engine for generating the sought volume meshes (TetWild).
•Quasi-immediate feedback of the structural performance is achieved
by structural analysis using nite element simulations based on the
generated volume mesh integrating realistic but computationally
efcient material models of sustainable biocomposite materials.
6. Outlook
While the proposed framework marks progress towards a more
cohesive workow incorporating material-informed structural feedback
in the early stages of design, further improvements in various directions
could overcome the current limitations and broaden its applicability
across a wider building engineering context.
•The geometric modelling module holds signicant potential for im-
provements. Currently, it outputs a single watertight triangular mesh
from the point cloud of the whole structure. However, it neither
segments the structure into its constituting elements, e.g., walls,
windows, etc. nor considers timestamp information that may help
interpreting the design intent throughout the reconstruction phase. A
potential workaround could be the implementation of a machine-
learning-based pipeline that utilises timestamp and other associ-
ated properties with strokes, which could output a richer geometric
format such as curve networks. This may also allow for the distinc-
tion of different elements forming the structure or building. Only
such an enriched geometric format would enable the integration of
other engineering domains in synchronization with structural feed-
back and would pave the way for Building Information Modelling
(BIM) interoperability.
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
10
Fig. 11. Material-informed structural analysis of the theatre stage wall and the pavilion as well as conceivable/feasible optimisation procedures. (a1), (a2) Initial FE-
structures with tetrahedral elements, loads, boundary conditions and material denitions. (b1) Visualisation of the deformed stage wall and (b2) Visualisation of the
von Mises stresses within the pavilion. (c1), (c2) Sensible material-informed structural optimisation and (d1), (d2) improved structural performance.
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
11
•Another limitation of our approach is that material models are
currently only implemented for the promising class of ber-
reinforced biocomposite materials. To make our system more ver-
satile, we plan to incorporate similar multiscale micromechanics
material models, which are available for more traditional building
materials including concrete [26] or clay bricks [8]. In addition,
current FE calculations are restricted to linear elasticity to keep the
computational efforts low. While this might be sufcient for early
design stages, more sophisticated constitutive material relations for
creep, plasticity and other nonlinear effects, and more efforts on
structural effects such as stability problems will allow the designer to
deal with more complex structures such as bridges.
•While the geometry, material modelling, and structural analysis are
currently separate from the sketching module, our goal is to seam-
lessly integrate them in the future. We envision a workow where
the designer can draw xed boundaries, sketch loads, and create new
materials all within the sketching tool. Additionally, we plan to
implement warnings for displacements or stresses that exceed certain
limits.
•Virtual and augmented reality approaches may further improve the
framework by creating an immersive and collaborative design
experience. Augmented reality would further allow for dealing with
already built structures and draw new designs on top of them.
All these ideas will enhance the usability and applicability of the
developed integrative design framework in a wider range of engineering
scenarios. Contrasting the traditional with the new integrative design
framework in a user study to obtain quantitative data on the claimed
benets will be an additional direction for future work, ideally in the
context of an industry collaboration.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Data availability
The data that has been used is condential.
Acknowledgements
The research is supported by grant F77 (SFB “Advanced Computa-
tional Design”, subprojects 2 and 8) as well as by the START grant Y1093
“Virtual Wood Labs” of the Austrian Science Fund (FWF). Moreover, the
authors thank the following subproject members for their contribution
and for providing valuable feedback:
● SFB, Subproject 2, Integrating AEC Domain Knowledge - Synthesis
2.0, Peter Ferschin, Ingrid Erb, Balint Istvan Kovacs, and Dalel
Daleyev.
● SFB, Subproject 8, Linking Mechanics to Form-Finding of Plant-
Based Bio-Composite Structures, Markus Lukacevic
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Table 1
Denitions, material composition, input parameters, and results for the two
“proof of concept”-examples in their initial and optimised state as seen in
Fig. 11.
Sketched
Geometry
Geometric
Features and
Boundary
Conditions
Material
Composition
Mechanical
Properties for
FEA*
Results
(a1)
Theatre Stage
Wall
L =7.20 m
B =0.32 – 0.38
m
H
1
=2.45 m
H
2
=4.20 m
α
1
=6◦
α
2
=20◦
F =1 kN
F
G
=m ⋅ g
BC: translation
of nodes on the
bottom plane
restricted
Flax-PP
composite
as in [41]
Isotropic
(randomly
distr. Fibres)
Fibre-volume
fraction: 10%
Porosity: 50%
E =1.93 Gpa
ν
=0.140
ρ
=511 kg/
m
3
u
max,0
=
32 cm
(c1)
Theatre Stage
Wall:
Reinforced
Part
Flax-PP
composite
as in [41]
Isotropic
(randomly
distr. Fibres)
Fibre-volume
fraction: 40%
Porosity: 0%
E =13.5 Gpa
ν
=0.273
ρ
=1142 kg/
m
3
u
max,1
=
12 cm
(a2)
Pavilion
L =20 m
B =0.30 m
H =3.80 m
F
G
=m ⋅ g
BC: translation
of nodes of all 3
bottom planes
restricted
Kenaf-PLA
biocomposite
as in
[66] Isotropic
(randomly
distr. Fibres)
Fibre-volume
fraction: 30%
Porosity: 0%
E =5.12 Gpa
ν
=0.277
ρ
=1260 kg/
m
3
σ
ult
=
54.5 Mpa
µ
0
>
200 %
**
u
max,0
=
34 cm
(c2)
Pavilion:
Optimised
Material
Orientation
Kenaf-PLA
biocomposite
as in
[66]
Transversely
Isotropic
(fully aligned
bres)
Fibre-volume
fraction: 30%
Porosity: 0%
E
‖
=29.0 Gpa
E
⊥
=5.45
Gpa
G
‖
=1.97
Gpa
G
⊥
=1.90
Gpa
ν
=0.287
ρ
=1260 kg/
m
3
σ
ult
=
149.0 Mpa
µ
1
~
100 %
**
u
max,1
=
11 cm
*obtained from the multiscale material model.
**maximum stress over strength ratio,
μ
=
σ
ult
σ
max (degree of utilisation).
S. Rasoulzadeh et al.
Advanced Engineering Informatics 57 (2023) 102074
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