Giovanni Garcea

Università della Calabria | Università della Calabria · Department of Computer Engineering, Modelling, Electronics and Systems (DIMES)

In this paper we show how to significantly improve the robustness and the efficiency of the Newton method in geometrically non-linear structural problems discretized via displacement-based finite elements. The strategy is based on the relaxation of the constitutive equations at each integration point. This leads to an improved iterative scheme whic...

The paper deals with two main advantages in the analysis of slender elastic structures both achieved through the mixed (stress and displacement) format with respect to the more commonly used displacement one: (i) the smaller error in the extrapolations usually employed in the solution strategies of nonlinear problems and (ii) the lower polynomial d...

In this paper we propose a powerful tool for the evaluation of the initial post-buckling behavior of multi-layered composite shells and beams in both bifurcation and limit load cases, including mode interaction and imperfection sensitivity. This tool, based on the the joint use of a specialized Koiter asymptotic method and a mixed solid-shell finit...

In this paper a semi-analytic solution for the post-critical behavior of compressed thin walled members with generic cross sections is presented. It is based on the Koiter approach and the method of separation of variables. The buckling solution is exactly evaluated using a single sinusoidal function and the initial post-critical behavior is obtain...

In this work an isogeometric solid-shell model for geometrically nonlinear analyses is proposed. It is based on a linear interpolation through the thickness and a NURBS interpolation on the middle surface of the shell for both the geometry and the displacement field. The Green–Lagrange strains are linearized along the thickness direction and a modi...

A generalized path‐following method is proposed for the direct evaluation of the critical point sensitivity to geometrical imperfections expressed as combination of given shapes. After a finite element discretization, the critical point is defined by a system of nonlinear algebraic equations imposing equilibrium and critical condition according to...

This work presents an accurate and efficient numerical tool for geometrically nonlinear thermoelastic analyses of thin‐walled structures. The structure is discretized by an isogeometric solid‐shell model with an accurate approximation of geometry and kinematics avoiding the parameterization of finite rotations. An efficient modeling of thermal stra...

This research investigates the formulation of a reduced modal space for the nonlinear dynamic seismic analysis of elasto-plastic 3D frame buildings. Starting from a full finite element model, the modal shapes of the reduced model for the kinematics are selected as the relevant linear elastic modes of the generalized stiffness/mass linear eigenvalue...

This work presents an accurate and efficient numerical tool for geometrically nonlinear thermoelastic analyses of thin-walled structures. The structure is discretized by an isogeometric solid-shell model with an accurate approximation of geometry and kinematics avoiding the parameterization of finite rotations. An efficient modeling of thermal stra...

Mixed assumed stress finite elements for elastic-perfectly plastic materials require the solution of a Closest Point Projection (CPP) involving all the element stress parameters for the integration of the constitutive equation. Here, a dual decomposition strategy is adopted to split the CPP at the element level into a series of CPPs at the integrat...

Mixed assumed stress finite elements have shown good advantages over traditional displacement-based formulations in various contexts. However, their use in incremental elasto-plasticity is limited by the need for return mapping schemes which preserve the assumed stress interpolation. For elastic-perfectly plastic materials and small deformation pro...

This study investigates a system for monitoring displacements of underground pipelines in landslide-prone regions. This information is an important alarm indicator, not only to prevent the failure of the line itself but also to mitigate the direct consequences of landslides on buildings and infrastructures in the affected area. Specifically, a nume...

Not all imperfections are detrimental in buckling problems. A recent design paradigm, termed modal nudging, utilizes geometric "imperfections" with negligible self-weight change to nudge the baseline structure onto equilibrium paths of greater load-carrying capacity. This paper is a contribution to this research line. Specifically, a simple automat...

A reduced order model for the nonlinear dynamic seismic analysis of elasto-plastic 3D frame structures is presented. It is based on an approximated solution space for the displacement field that is assumed as the sum of two subspaces. The first subspace is generated by the relevant linear elastic modes of the generalized stiffness/mass linear eigen...

Stability is a fundamental feature of a time integration method in long simulations of elastic bodies in large deformations. It is well known that energy conservation is the key to achieve it. The implicit one-step conserving method of Simo and Tarnow is simple and effective for quadratic strain measures. However, the issue of unconditional stabili...

An efficient continuation method is proposed for a direct sensitivity analysis of the critical point to geometrical imperfections, e.g. expressed as combination of given shapes, for thin-walled structures prone to buckling. After a finite element discretization, the critical point is defined by a system of nonlinear algebraic equations imposing equ...

The multi-modal Koiter method is a reduction technique for estimating quickly the nonlinear buckling response of structures under mechanical loads requiring a fine discretisation. The reduced model is based on a quadratic approximation of the full model using a few linear buckling modes and their second order corrections, followed by the projection...

This work introduces a mathematical problem named limit fire analysis for estimating the structural safety of 3D frames in case of fire, taking into account the stress redistribution. It is a generalization of the classic limit analysis to a fire event, where the load factor is replaced by the time of fire exposure that reduces the strength of the...

Lightweight thin-walled structures are crucial for many engineering applications. Advanced manufacturing methods are enabling the realization of composite materials with spatially varying material properties. Variable angle tow fibre composites are a representative example, but also nanocomposites are opening new interesting possibilities. Taking a...

This work presents a cost-effective and reliable numerical framework for geometrically nonlinear thermoelastic analyses of thin-walled structures. Firstly, the structure is discretised using an isogeometric solid-shell formulation, that allows an accurate approximation of geometry and kinematics avoiding the parameterisation of finite rotations. Fo...

The starting point of this work is the definition of an automatic procedure for evaluating the axial force-biaxial bending yield surface of steel and reinforced concrete sections in fire. It provides an accurate time-dependent expression of the yield condition by a section analysis carried out once and for all, accounting for the strength reduction...

In large rotation analysis of shear deformable 3D beams, some features characterize the ideal discretization method: locking-free solution, small number of unknowns, accurate description of curved geometries, no singularity for large rotations, objectivity, additivity and robustness in the iterative solution, path independence and symmetric matrix...

Carbon nanotube/polymer nanocomposite plate- and shell-like structures will be the next generation lightweight structures in advanced applications due to the superior multifunctional properties combined with lightness. Here material optimization of carbon nanotube/polymer nanocomposite beams and shells is tackled via ad hoc nonlinear finite element...

The optimal design of the postbuckling response of variable angle tow composite structures is an important consideration for future lightweight, high-performing structures. Based on this premise, a new optimisation tool is presented for shell-type structures. The starting point is an isogeometric framework which uses NURBS interpolation functions t...

Isogeometric Kirchhoff–Love elements have been receiving increasing attention in geometrically nonlinear analysis of thin shells because they make it possible to meet the C1 requirement in the interior of surface patches and to avoid the use of finite rotations. However, engineering structures of appreciable complexity are typically modeled using m...

It is with profound sadness that we share the news that Prof. Raffaele Casciaro passed away on 27 July 2020. He is buried in his beloved Rossano, a small city in southeast Italy, where he was born in 1943. It is not easy to describe, in just a few sentences, the extraordinary human and scientific personality of Raffaele. He was an unattainable mode...

This work presents an efficient fiber analysis for evaluating the shakedown safety factor of three‐dimensional frames under multiple load combinations. Mixed finite elements are employed for an accurate discretization. A continuation method, similar to a standard elasto‐plastic analysis, is used at structural level. It evaluates a pseudo‐equilibriu...

The optimisation of the structural behaviour of the wing is one of the key aspects in the design of future aircraft. Enhanced freedom to designers has been offered by the stiffness-tailoring capability of Variable Angle Tow (VAT) laminates. Efficient and robust optimisation strategies are, consequently, of great importance to fully explore such an...

Different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing beams undergoing large rotations. The interpolation of the total rotation vector is path independent but also singular at the full angle and non objective. The interpolation of the incremental rotation vector avoids the singularity...

Different strategies based on rotation vector and exact strain measure have been proposed over the years for analyzing exible bodies undergoing arbitrary large rotations. To avoid the singularity of the vector-like parametrization, the interpolation of the incremental rotation vector is the most popular approach in this context, even if this leads...

Variable Angle Tow (VAT) laminates have notably enhanced the possibilities of tailoring the stiffness properties of thin-walled structures. This increased freedom meets the need for designing lighter-weight structures. Consequently, buckling and postbuckling phenomena often lead the structural response and have to be considered from the preliminary...

Isogeometric Kirchhoff-Love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells. Nevertheless, some difficulties still remain. Among the others, the highly nonlinear expression of the strain measure, which leads to a complicated and costly computation of the discrete operators, and the existence of l...

The optimisation of the structural behaviour of the wing is one of the key as- pects in the design of future aircraft. Enhanced freedom to designers has been offered by the stiffness-tailoring capability of Variable Angle Tow (VAT) laminates. Efficient and robust optimisation strategies are, consequently, of great importance to fully ex- plore such...

The stiffness-tailoring capability of Variable Angle Tow (VAT) laminates gives enhanced freedom to designthin-walled structures. One key advantage of tow steering is the ability to redistribute stresses improving buckling performance, leading to reduction in material weight and costs. The aim of this work is to optimise the initial postbuckling beh...

A new computational strategy for the elasto-plastic analysis of framed structures is proposed. The approach is composed of two levels of analysis: the frame level, based on a 3D mixed beam element, and the cross-section level, described through the Generalized Eigenvectors approach whose formulation is here extended for the analysis of materials wi...

The paper concerns mixed finite element models and experiments their capability in the analysis plastic collapse of both plane and three-dimensional problems respectively. The models are easy to formulate and implement because are based on simple assumptions for the unknown fields. A composite triangular or tetrahedral mesh is assumed over the doma...

This work makes the Minkowski sum of ellipsoids into a consolidated tool for the representation of the yield surface of arbitrarily shaped composite cross‐sections under axial force and biaxial bending and shows how best to use it within the incremental nonlinear analysis of 3D frames. A geometric interpretation of each term of the sum allows us to...

Numerical formulations of the Koiter theory allow the efficient prediction, through a reduced model, of the behavior of shell structures when failure is dominated by buckling. In this work, we propose an isogeometric version of the method based on a solid-shell model. A NURBS interpolation is employed on the middle surface of the shell to accuratel...

A numerical stochastic strategy for the optimisation of composite elastic shells undergoing buckling is presented. Its scope is to search for the best stacking sequence that maximises the collapse load optimising the post-buckling behaviour. Its feasibility is due to a reduced order model built for each material setup starting from a hybrid solid-s...

The classical Eurocode-compliant ultimate limit state (ULS) analysis of reinforced concrete sections is investigated in the paper with the aim of verifying if and how this well-established design procedure can be related to plasticity theory. For this reason, a comparative analysis concerning capacity surfaces of reinforced concrete cross sections,...

In this paper, an alternative formulation of the NS-FEM based on an assumed stress field is presented to include drilling rotations. Within each triangular element the displacement field is described by a revised Allman triangle interpolation, while the stress field is assumed as linear or linear reduced on the conflict domain of the background gri...

The Koiter method recovers the equilibrium path of an elastic structure using a reduced model, obtained by means of a quadratic asymptotic expansion of the finite element model. Its main feature is the possibility of efficiently performing sensitivity analysis by including a-posteriori the effects of the imperfections in the reduced non-linear equa...

The paper concerns mixed finite element models and experiments their capability in the analysis plastic collapse of both plane and three-dimensional problems respectively. The models are easy to formulate and implement because are based on simple assumptions for the unknown fields. A composite triangular or tetrahedral mesh is assumed over the doma...

The Koiter-Newton method had recently demonstrated a superior performance for nonlinear analyses of structures, compared to traditional path-following strategies. The method follows a predictor-corrector scheme to trace the entire equilibrium path. During a predictor step, a reduced-order model is constructed based on Koiter's asymptotic postbuckli...

The Koiter method recovers the equilibrium path of an elastic structure using a reduced model, obtained by means of a quadratic asymptotic expansion of the finite element model. Its main feature is the possibility of efficiently performing sensitivity analysis by including a-posteriori the effects of the imperfections in the reduced non-linear equa...

We propose a mixed smoothed finite element model for plane elasticity. Within each triangular element the displacement field is described by a revised Allman interpolation, while the stresses are assumed to be piece-wise constant on a background grid associated with the edges of the triangle. A straightforward implementation of the element, in orde...

The paper proposes a 3D mixed finite element and tests its performance in elasto-plastic and limit analysis problems. A composite tetrahedron mesh is assumed over the domain. Within each element the displacement field is described by a quadratic interpolation, while the stress field is represented by a piece-wise constant description by introducing...

This paper compares two distinct approaches for obtaining the cross-section deformation modes of thin-walled members with deformable cross-section, namely the method of Generalized Eigenvectors (GE) and the Generalized Beam Theory (GBT). First, both approaches are reviewed, emphasizing their differences and similarities, as well as their resulting...

A new iterative algorithm to evaluate the elastic shakedown multiplier is proposed. On the basis of a three field mixed finite element, a series of mathematical programming problems or steps, obtained from the application of the proximal point algorithm to the static shakedown theorem, are obtained. Each step is solved by an Equality Constrained Se...

Using the Melan static theorem and an algorithm based on dual decomposition, a formulation for the shakedown analysis of 3D frames is proposed. An efficient treatment of the load combinations and an accurate and simple definition of the cross-section yield function are employed to increase effectiveness and to make shakedown analysis an affordable...

A new geometrically nonlinear model for homogeneous and isotropic beams with generic section including non-uniform warping due to torsion and shear is derived. Each section is endowed with a corotational frame where statics and kinematics are described using a 3D linear elastic model which extends the Saint-Venant solution to non-uniform warping ca...

A model for beams with heterogeneous and anisotropic cross-section is presented. A semi-analytical approach which exploits a FEM discretization of the cross-section is used to derive a Ritz–Galerkin approximation of the stress and displacement fields. In this way the Saint-Venant solution is easily generalized to generic composite sections and addi...

A linear model for beams with compact or thin-walled sections and heterogeneous anisotropic materials is presented. It is obtained by means of a Ritz–Galerkin approximation using independent descriptions of the stress and displacement fields. These are evaluated by a preliminary semi-analytic solution based on a finite element description of the cr...

The analysis of slender structures, characterized by complex buckling and postbuckling phenomena and by a strong imperfection sensitivity, is heavily penalized by the lack of adequate computational tools. Standard incremental iterative approaches are computationally expensive and unaffordable, while FEM implementation of the Koiter method is a conv...

The analysis of slender structures, characterized by complex buckling and postbuckling phenomena and by a strong imperfection sensitivity, is heavily penalized by the lack of adequate computational tools. Standard incremental iterative approaches are computationally expensive and unaffordable, while FEM implementation of the Koiter method is a conv...

A new linear model for beams with compact or thin-walled section is presented. The formulation is based on the Hellinger–Reissner principle with independent descriptions of the stress and displacement fields. The kinematics is constituted by a rigid section motion and non uniform out-of-plane warpings related to shear and torsion. The stress field...

A geometrically nonlinear model for isotropic and homogeneous beams including the non-uniform out of plane warping deformation of the cross-section due to torsion and shear is derived using the implicit corotational method (ICM). The basic idea of ICM is the application of the corotational method, initially proposed for a whole finite element, at l...

A mathematical programming formulation of strain-driven path-following strategies to perform shakedown and limit analysis for perfectly elastoplastic materials in a FEM context, is presented. From the optimization point of view, standard arc–length strain driven elastoplastic analysis, recently extended to shakedown, are identified as particular de...

A new method for the incremental elastoplastic analysis of structures is presented. Retaining all the equations and variables of the problem at the same level, a particular implementation of sequential quadratic programming with equality constraints is applied to solve the elastoplastic step. The proposed method and standard strain driven formulati...

What we call the implicit corotational method is proposed as a tool to obtain geometrically exact nonlinear models for structural elements, such as beams or shells, undergoing finite rotations and small strains, starting from the basic solutions for the three-dimensional Cauchy continuum used in the corresponding linear modelings. The idea is to us...

What we call the implicit corotational method is proposed as a tool to obtain geometrically exact nonlinear models for structural elements, such as beams or shells, undergoing finite rotations and small strains, starting from the basic solutions for the three-dimensional Cauchy continuum used in the corresponding linear modelings. The idea is to us...

In our previous paper the implicit corotational method (ICM) was presented as a general procedure for recovering objective nonlinear models fully reusing the information obtained by the corresponding linear theories. The present work deals with the implementation of the ICM as a numerical tool for the finite element analysis of nonlinear structures...

A mathematical programming formulation of strain-driven path-following strategies to perform shakedown and limit analysis for perfectly elastoplastic materials in an FEM context is presented. From the optimization point of view, standard arc-length strain-driven elastoplastic analyses, recently extended to shakedown, are identified as particular de...

A three field variational framework is used to formulate a new class of mixed finite elements for the elastoplastic analysis of 2D problems. The proposed finite elements are based on the independent interpolation of the stress, displacement and plastic multiplier fields. In particular new and richer interpolating patterns are proposed for the plast...

Such we call Implicit Corotational Method, is proposed as a tool to obtain geo-metrically exact nonlinear models for structural elements, such as beams or shells, undergoing nite rotations and small smooth strains starting from the basic solutions for the 3D Cauchy continuum used in the corresponding linear modelings. The idea is to use a local cor...

A new method for the incremental analysis of elastoplastic associated materials is presented. The method fully retains all the equations and variables of the problems at the same level and uses a sequential quadratic programming with equality constraints to solve in an efficient and robust fashion the elastoplastic step equations derived by means o...

A new method for the incremental analysis of elastoplastic associated materials is presented. The method fully retains all the equations and variables of the problems at the same level and uses a sequential quadratic programming with equality constraints to solve in an efficient and robust fashion the elastoplastic step equations derived by means o...

Two kinds of mixed elements for the analysis of elastoplastic problems are presented. The elements are 2D quadrangular finite elements whose variational framework is based on the weak statement of the equilibrium, compatibility and of the plastic loading-unloading conditions. In this context the interpolation of three fields is required: displaceme...

Keywords: Implicit Corotational Method (ICM), geometrically exact beam and plate models, mixed finite elements, asymptotic and path–following analyses. Abstract. The Implicit Corotational Method (ICM) is a powerful and consolidated approach for recovering frame invariant nonlinear models. An appropriate stress/strain (Biot) represen-tation for the...

Finite element asymptotic post-buckling analysis, being based on fourth-order expansions of the strain energy, requires that nonlinear structural modeling be accurate to same order, at least with respect to the rigid motions of the elements. A corotational description is proposed here as a general tool to satisfy this requi