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Parametric Finite Element Contact Analysis for Topologically Interlocking Joinery
Abstract and Figures
Topologically Interlocking Joineries (TIJs) can be viewed as a design principle to join structural elements without metallic fasteners by creatively using topology/geometry to create interlocking structures. TIJs are found in traditional timber structures, ecologically viable buildings with a long history both in Eastern and Western culture. Such joints developed and refined over centuries exhibits enormous body of material knowledge as well as care and perfection in craftsmanship (ex. Brown [1]; Hamajima, et al. [2]; Nakahara, et al. [3]). However, today, the number of constructions using TIJs is decreasing for multiple reasons including the insufficient scientific understanding of the structural behavior of such joinery (Architectural institute of Japan, [4]). In the context stated above, our multidisciplinary research project between architecture and mechanical engineering aims to advance the understanding and designs of TIJs in light of new simulation and fabrication methods. The particular paper focuses on the development of parametric contact analysis. A full 3D finite element models were created to gain insight into the mechanical behavior of the TIJs. Building such model involves solid modeling of the geometry, creation of finite element mesh appropriate for the analysis, assignment of contact interactions, and selection of parameters to be explored. The relationships between critical geometric parameters and joint stiffness will be discussed alongside two TIJ case studies.
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... Efforts in performing numerical analysis for uncommon TIJs and developing new/extended joinery designs are still extremely limited. In previous work (Kaijima et al. [12]), we presented a parametric study of two uncommon TIJs, during which we revealed the critical geometric variables contributing to their structural behavior. More specifically, we looked at improving the overall stiffness of the TIJs under various loading conditions. ...
... The geometry for the study was built as an assembly of 2 liner parts (Figure 1, A and B) with a joint in the middle (C); approximately 1500mm for each part, 3000mm long when assembled, with a square cross-section of 400mm, the long side of the assembly aligns to Z-axis of the model. The geometric variables Wt, Wb and ht, selected in the previous study (Kaijima et al. [12]), were reconsidered in this parametric model and allowed to vary independently of each other. The bottom surface of the lower element (B) was fixed in all 6 degrees of freedom (Figure 3). ...
... The model assumes ABAQUS " general contact interaction " between the parts and the interface was modeled using the Coulomb friction contact algorithm available in ABAQUS with a friction coefficient µ = 0.5 and contact pressure-over-closure was set to " Hard " which minimizes the penetration of the slave surface into the master surface at the constraint locations (ABAQUS). The same mesh characteristics from the previous study (Kaijima et al. [12]) were used. ...
The paper presents an approach to parametric finite element contact analysis and optimization of Topologically Interlocking Joineries (TIJs) utilizing the Design of Experiments (DOE) statistical technique. TIJs can be viewed as a design principle to join structural elements without metallic fasteners by using topology/geometry and contact mechanisms to create interlocking structures. Simulations of such joints require full 3D finite element models with contact interactions, which are computationally expensive thus time consuming to execute optimizations. In this context, we suggest the application of DOE to perform an efficient search through the design/variable space. This paper presents a case study on a TIJ called Basra Splice. This study revealed variable sensitivity that was not discovered in our previous paper (Kaijima [12]). Moreover, DOE helped us gain further insights into the relationship between the geometrical variables and the structural behavior of the TIJ by estimating variable sensitivities and variable correlations.
... Recently, some researchers started to perform experiments on available joints to study the physical behavior of TIJs under mechanical loadings Chang et al. [1], Suzuki and Maeno [9], and Maeno and Suzuki [8]. Moreover, some other efforts on developing simplified structural calculation and numerical analysis of simple joint systems are reported Guan et al. [3], Jeong et al. [5], Kaijima et al. [6], Takino [10], Tannert et al. [11], and Tannert et al. [12]. ...
Topologically interlocking joineries (TIJs) are structures that connect different parts by using only the geometry and topology of the contact area. Owing to new manufacturing facilities such as 3D printers, new attention toward TIJs increased in recent years. However, there is a lack of structural analysis and application of joints in large-scale structures for current designs. In this study, to reduce the complexity of three-dimensional analysis of large-scale structural simulations, TIJs are replaced with proposed new user-defined elements developed and implemented to be used with finite element software, ABAQUS. Furthermore, the accuracy of this method is discussed by comparing the results of the proposed model and full-solid elements model. Finally, case studies are presented to illustrate the application of this method in the large-scale structural analysis.
Multi-material additive manufacturing processes enable the fabrication of 3D objects composed of varying material properties at microscopic scale (Doubrovski et al. [7]). Selective material deposition offers opportunities to design and fabricate objects with heterogonous properties potentially exhibiting superior functional performance characteristics compared to objects comprised of homogenous material distributions (Wu, et al. [23]). Despite the availability of 3D printing hardware capable of producing such objects, access to this new technology is encumbered by the way in which the current modelling and simulation tools represent, exchange, and process information required for multi- material additive manufacturing. We present a computation-based approach for fabricating Functionally Graded Designs (FGD) based on solid Finite Element (FE) analysis results using Multi- Material Voxel Printing technology.
The most common connection in historic green oak framing vernacular architecture is the all-timber pegged mortice and tenon joint. This paper outlines a series of tests completed to investigate the pull-out, bending and shear behaviour of the mortice and tenon joint. Initially strength and stiffness characteristics of different peg types subject to pull-out (joint tension) loading and the effect of fit tolerance on pull-out performance of mortice and tenon joints are reported. Thereafter joint moment resistance and shear capacity tests are reported and links between the pull-out performance and rotational stiffness discussed. Finally, a series of braced subframe tests are reported, to which upper-bound plasticity theory is successfully applied to predict collapse load.
Previous studies have shown that double shear timber connections with glass fibre reinforced polymer dowels are a viable alternative to metallic timber connections. Different models have been proposed for predicting the load capacity of the connection. A model which accurately predicts stiffness for connections of this type is, however, not yet published. This paper discusses a two dimensional linear finite element model that predicts the slip modulus of non-metallic timber connections made with pultruded dowels. The model is compared to experimental results and it is concluded that the two dimensional model is accurate.
Initial conditions introduced by different wedges in a traditional Japanese “Nuki” joint affect its stiffness and load carrying capacity significantly. Due to the complicated nature of the problem, no proper measurements have been undertaken historically, nor has there been theoretical modeling of the initial stress state in the joint. This leads to a lack of full understanding in the critical regions where high contact stresses are generated by locking wedges into various engaged positions. There is a need to undertake quantitative studies in those regions in order to make better designs and assist renovation of this type of the joint. In the work described in this paper, a series of experiments has been undertaken to investigate initial strain (and hence stress) states of the “Nuki” joint induced by the use of wedges with a typical angle but various tightnesses. A large number of strain gauges were used to obtain strain distributions in critical areas of the “Nuki” beam element. In Part 1 of the paper, 3-D nonlinear finite element models were developed to simulate the wedge insertion processes and the initial strain (stress) states. Numerical simulations were compared with the corresponding experimental results yielding reasonably good correlation. Racking resistance of the “Nuki” joint will be presented in Part 2.
The strength prediction of rounded dovetail connections (RDCs), a relatively new connection for structural timber members, is difficult due to the anisotropic and brittle nature of the material, the complex stress distribution as well as the uncertainties regarding the associated material resistance. Experimental investigations were carried out to provide input and benchmark data for developing a method to predict RDC strength. Numerical analyses confirmed that the experimentally observed failure location was also the highest stressed part of the model. A probabilistic method is presented to predict the strength of RDC. The method, rather than being stress-based, incorporates size effect for the combined action of tension perpendicular to grain and shear parallel to grain stresses in timber by comparing computed stress volume integrals to unit volume strength thresholds. Therefore not only the magnitude of the stress distributions is considered but also the volume over which they act. The capacities of RDC configurations were predicted and successfully validated with experimental tests. The presented strength prediction method has immediate application for the improvement of RDC design.
The paper gives a bibliographical review of finite element methods applied for the analysis of fastening and joining from the theoretical as well as practical points of view. The bibliography at the end of the paper contains 726 references to papers and conference proceedings on the subject that were published between 1990 and 2002. These are classified in the following categories: pin joints; thread connections; bolted joints, screws, nuts; rivets; fittings; tubular joints; expansion joints; gaskets; and other types of fastening.
The Genius of Japanese Carpentry: The Secrets of a Craft
- A Brown
Brown, A., The Genius of Japanese Carpentry: The Secrets of a Craft, Oxford University Press,
1978, ISBN 4-7700-1978-5.