Rotation-Free Based Numerical Model for Nonlinear Analysis of Thin Shells

This thesis presents new numerical models for analysis of thin beam and arch structures and thin plate and shell structures based on the combined finite-discrete element method (FDEM). The new models perform quasistatic and dynamic analysis. The thesis also presents an overview of the established numerical tools for the analysis of arch and shell structures, together with their strengths and disadvantages. The bases of the combined finite-element method and its strengths are also presented. The main motivation was the development of precise, robust and computationally efficient numerical models. The model for the analysis of thin beam and arch structures uses straight two-noded rotation free finite elements, and takes into account linear-elastic material behaviour, finite displacement, finite rotations and small strains. The thesis describes axial and bending carrying mechanisms of a beam finite element in detail. The presented model is implemented into the open source FDEM package ‘Yfdem’. Performance of the new numerical model is demonstrated on simple benchmark tests by a comparison with known analytical and numerical results. Its application for the seismic analysis of arch structures is presented. This thesis also presents a new numerical model for analysis of thin plate and shell structures. The model uses three-noded triangular finite elements, and takes into account linear-elastic material behaviour, finite rotations, finite displacements and small strains. The thesis describes membrane and bending carrying mechanisms for triangular finite element in detail. The model is implemented into the open source FDEM package ‘Yfdem’. Performance of the new numerical model was demonstrated on simple benchmark tests by comparing it with the known analytical and numerical results. Its application in typical problems of stability of plate and shell structures is presented. Directions for further development and upgrade of the model in performing contact interaction and material nonlinearity are given.

PurposeThis paper aims to present a new numerical model for geometric nonlinear analysis of thin-shell structures based on a combined finite-discrete element method (FDEM).Design/methodology/approachThe model uses rotation-free, three-node triangular finite elements with exact formulation for large rotations, large displacements in conjunction with small strains.FindingsThe presented numerical results related to behaviour of arbitrary shaped thin shell structures under large rotations and large displacement are in a good agreement with reference solutions.Originality/valueThis paper presents new computationally efficient numerical model for geometric nonlinear analysis and prediction of the behaviour of thin-shell structures based on combined FDEM. The model is implemented into the open source FDEM package “Yfdem”, and is tested on simple benchmark problems.

Classical linear contact mechanics, formulated with small strain and displacement assumption, struggles to accurately describe experiments involving rubbers and elastomers. Indeed, under high loads, these materials undergo large deformations and exhibit constitutive behaviors that deviate from a linear relationship between stress and strain. In such cases, it is essential to move beyond linear elasticity to account for nonlinearity caused by large deformations and displacements. Despite efforts to develop numerical tools capable of incorporating these non-linearities in contact problems, our understanding of their impact on contact mechanical responses remains limited. In this study, we investigate the basic case of normal contact between a wavy rigid indenter and a flat, deformable substrate. We examine the influence of geometric non-linearities, arising from large deformations and displacements, alongside material non-linearities, under both frictionless and frictional interfacial conditions. To this end, we developed a finite element model, and we compared its predictions with those of Westergaard’s fully linear theoretical model. The results indicate that even in frictionless contact scenarios, non-linearities produce a mechanical response that differs significantly from predictions based on linear theory. This discrepancy becomes more pronounced as the aspect ratio of the wavy indenter increases, thereby invalidating the small-displacement assumption inherent in linear models. Moreover, the presence of friction, coupled with geometric non-linearities, induces contact hysteresis during loading and unloading cycles a phenomenon often attributed to other interfacial behaviors such as adhesion and plasticity.

In Chapters 4 to 6 it was assumed that contact bodies undergo only small displacements and thus small rotations and small deformation. Consequently, we restricted ourselves to only a special class of contact-impact problems. In engineering applications, however, there are many extremely important contact-impact problems that cannot be included in that special class. In metal-forming processes, for example, workpieces may undergo quite large displacements, large rotations, and large deformation. Thus the behaviour of the workpiece presents both geometric non-linearity and material non-linearity. Many assumptions made in Chapters 4 to 6 no longer apply. Instead, we have to use the more general formulation in Chapter 3.

This paper concerned the stamping process of corrugated sheet metal for sealing device honeycomb manufacturing. GH536 foil with a thickness of 0.05mm was used to produce corrugated sheet metal with semi-hexagonal profile. Finite element models for the corrugated sheet metal stamping process were built to analyze the forces and material deformation. The prototype molds with a pair of pressure dies were designed and tested. Then according to the curling phenomenon occurred in the experimental result of prototype molds, the optimized final molds was designed with three pairs of pressure dies. The formed corrugated sheet metal by the final molds was much better. KEYWORD: Corrugated metal sheet; Stamping; Honeycomb manufacturing; Numerical simulation International Conference on Industrial Technology and Management Science (ITMS 2015) © 2015. The authors Published by Atlantis Press 1281 The demanded specifications of the corrugated sheet metal is shown in Figure 2, the angles between adjacent sides θ1=θ2 =120°, side length l1 = l2 = l3 = 0.8mm, thickness t=0.05mm. Figure 2. The demanded specifications of the corrugated sheet metal 2 NUMERICAL SIMULATION The principle of stamping is that the part with desired shape and size is obtained by a method of permanent plastic deformation of work piece. This process is achieved by the normal contact force and tangential frictional forces between the mold and the work piece. The stamping process involves three nonlinear problems in mechanics. (1) Geometric nonlinearity (Large displacement, rotation and deformation in the stamping process). (2) Physical nonlinearity (Also known as material nonlinearity which refers to elastic-plastic deformation of the material). (3) Boundary nonlinearity (Refer to non-linear relationship caused by contact friction between the die and work piece). The development of computer technology and finite element method provides a new way for complex engineering calculation. This paper used explicit dynamic software ANSYS\LS-DYNA to simulate the corrugated sheet metal stamping process 2.1 Original Design of Stamping Molds For the corrugated sheet metal stamping, special molds was designed as illustrated in Figure 3 and Figure 4. All the fillets are 0.1 mm. The material of the molds is P20 # steel. Since the GH536 foil is very thin, the deformation of molds is negligible in the forming process, so the molds can be regarded as rigid in simulation. The material properties of the molds are listed in Table 3. Figure 3. Illustration of upper die Figure 4. Illustration of lower die Table 3 The material properties of the molds Desinty (g/cm 3 ) Elastic Modulus (GPa) Possion’s ratio 7.8 206 0.3 The finite element model is illustrated in Figure 5. The molds were modeled using solid elements, and the foil was modeled using shell elements. The foil feed from the left with a preset motion, and the rigid molds moved in vertical direction. The foil and rigid molds were constrained to prevent undesired motion. Two stamping steps were simulated to form two semi-hexagonal profiles. The calculation time was set to 0.3s. The simulated stamping process is shown in Figure 6.

Owing to their low induced drag, high-aspect-ratio wings are often applied to aircraft, particularly high-altitude long-endurance (HALE) aircraft. An analytical method that considers geometrical nonlinearity is necessary for the analysis of high-aspect-ratio wings as they tend to undergo large deformations. Nonlinear shell/plate or solid finite element methods are widely used for the static analysis of wing strength. However, an increase in the number of elements drastically increases the computational costs owing to the complexity of wing shapes. The modal rotation method (MRM) can avoid this additional expense by analyzing large deformations based on modes and stiffness matrices obtained from any linear or linearized model. However, MRM has only been formulated as a static analysis method. In this study, a novel modal-based dynamic analysis framework, referred to as dynamic MRM (DMRM), is developed to analyze slender cantilever structures. This paper proposes a method to discretize dynamics by capitalizing on the fact that MRM considers geometrical nonlinearity based on deformed shapes. The proposed method targets slender structures with small strains and large displacements and considers geometrical nonlinearity, but not material nonlinearity. Additionally, a formulation method for the work performed by a follower force is proposed. The energy stored in the structure agreed with the work performed by an external force in each performed simulation. DMRM achieved a 95% reduction in the calculation time compared with a nonlinear plate finite element method in a performed simulation.

In this paper, numerical analysis of several historical masonry towers located in Italy was conducted. The towers differ in their geometric characteristics in terms of slenderness, thickness of the outer walls, the proportion of openings, while the material properties of all towers are similar. The purpose of this paper was to analyse the influence of various geometries, soil properties and types of earthquakes on the seismic resistance of masonry structures. The geometries of the towers were taken from the available literature. The analysis was carried out with the planar numerical model Y-2D, which is based on the finite-discrete element method (FDEM). The towers were discretized at the macro level using triangular three-node finite elements between which contact elements were implemented that take into account material nonlinearity. The discretization of the towers was carried out at the macro level, taking into account the averaged properties of the mortar and blocks. This is modelled using triangular three-node finite elements between which contact elements are implemented to consider material nonlinearity. In this way, the phenomenon of the initiation and propagation of cracks in the tension and shear was modelled. An incremental dynamic analysis was performed for three real earthquakes until the complete collapse of the structure. In each increment, the appearance of the first cracks, the propagation of the cracks, as well as the failure mode of the structure were monitored. The performed numerical analyses highlight the suitability of the FDEM method in the analysis of the seismic resistance of masonry structures. The conclusions reached in this paper can serve as guidelines for engineers in assessing the seismic resistance of existing masonry structures.

A refined non-conforming triangular plate/shell element for linear and geometrically nonlinear analysis of plates and shells is developed in this paper based on the refined non-conforming element method (RNEM). A conforming triangle membrane element with drilling degrees of freedom in Cartesian coordinates and the refined non-conforming triangular plate-bending element RT9, in which Kirchhoff kinematic assumption was adopted, are used to construct the present element. The displacement continuity condition along the interelement boundary is satisfied in an average sense for plate analysis, and the coupled displacement continuity requirement at the interelement is satisfied in an average sense, thereby improving the performance of the element for shell analysis. Selectively reduced integration with stabilization scheme is employed in this paper to avoid membrane locking. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear analysis of plate bending problems and plane problems or for the geometrically nonlinear analysis of thin plates and shells with large displacement, moderate rotation but small strain.

ABSTRACT: The goal of this paper is to present recent developments aimed at improving computational efficiency and extending the range of material applicability of a 2D/3D FDEM geomechanical simulation software. Firstly, a hybrid FEM-FDEM logic was devised to allow for user-defined regions of the domain to be modeled as a continuum, while the remainder is captured by the FDEM formulation with an intrinsic cohesive zone model explicitly capturing fracturing. Benchmarking results indicate simulation speed-ups of up to 48x when using the new logic versus the traditional full FDEM approach. Secondly, the finite element formulation was enhanced with elasto-plastic constitutive models based on Drucker-Prager and Mohr-Coulomb failure criteria, effectively broadening the range of applicability to materials that exhibit irreversible damage processes under load without breaking. These developments were initially verified by comparing simulated stress distributions against analytical solutions for select boundary value problems. Practical validation of the novel FDEM formulation was achieved by capturing the variation of critical failure mechanism observed in a slope as a function of the type of rock mass jointing. The factors of safety computed with the strength reduction method compared very well with those reported in the literature for commercially available programs based on DEM and FEM. Finally, a direct comparison between FEM-based, elasto-plastic and FDEM-based, brittle-fracture models is presented for the case of a homogeneous rock slope. 1. INTRODUCTION The finite-discrete element method (FDEM) is a numerical method originally introduced by Munjiza et al. (1995) as a means of combining principles of continuum mechanics, such as the theory of elasticity and non-linear fracture mechanics, with discrete element algorithms to model fracture, fragmentation, and failure of cementitious materials and rocks. Building upon Munjiza's pioneering work, FDEM has been further developed by a multitude of research groups and organizations worldwide, and applied to a variety of rock mechanics and rock engineering problems where consideration of brittle fracturing processes is critical. Over the years, developments of FDEM have focused on several major areas of interest including (i) improvement of the core algorithms for deformation, fracture, interaction, and contact detection (e.g., Lei et al., 2016, Fukuda et al., 2021, Cai et al., 2023), (ii) incorporation of multi-physics capabilities to account for hydraulic and thermal effects (e.g., Yan and Jiao, 2018, Yan et al., 2019, Munjiza et al., 2020), and (iii) reduction of simulation run times by parallel computing (e.g., Lei et al., 2014; Lisjak et al., 2018; Fukuda et al, 2019). In the classic implementation of FDEM (Munjiza, 2004), the numerical representation of fractures is achieved by an intrinsic cohesive zone model (ICZM). With this approach, zero-thickness cohesive crack elements are inserted (at the beginning of the simulation) across pairs of adjacent solid finite elements throughout the entire modelling domain. All irreversible ("plastic") deformations are concentrated in the form of yielding and breakage of the interfaces between the solid finite elements, which remain elastic.

CALEB is a nonlinear finite element program for geometric and material nonlinear analysis of offshore platforms and general framed structures. The finite element formulations implemented in CALEB assumes large displacements and small strain. Geometric nonlinearity is taken into account by means of an updated Lagrangian formulation. Material nonlinearity is taken into account by means of an elastic perfectly plastic model derived from plastic hinge theory. Capabilities of CALEB version 1.4, the current release of CALEB, include: pre-processor for mesh refinement, problem-oriented language input, distributed member loads, automatic generation of environmental loads, joint failure check, save/restart procedure, eigenvalue buckling analysis, nonlinear stress analysis, and graphical post- processing. In this paper a brief description of CALEB version 1.4 and of its main features is presented.

Finite element modelling of cold-formed steel beams under local buckling or combined local/distortional buckling

Adhesive joints serve under thermal loads as well as structural loads. The different thermo-mechanical properties of the adhesive and adherend materials cause incompatible thermal strains along the adhesive and adherend interfaces. Consequently, nonuniform thermal stress distributions are observed in the adhesive joints. In case the adhesive joints are constrained, these thermal stresses become more evident even for a uniform temperature distribution. In practice the adhesive joints interact with fluids (air) with different temperature and velocity and experience conductive and convective heat transfers. The variable thermal boundary conditions introduce a new non-linearity in addition to the geometrical and material non-linearities which are observed in adhesive joints. The transient temperature distributions can be obtained by solving the energy equation under the thermal boundary conditions. The corresponding thermal strain and stress distributions can be calculated using the transient temperature distributions. The large displacement and rotations occurring in adhesive joints require the implementation of the small strain-large displacement theory to the elastic stress analysis. This study introduces a simple method for calculating the heat transfer coefficients between the fluid and adhesive joints and explains the implementation of the finite element method to the thermal analysis and the geometrical nonlinear stress analysis. The thermal stresses in the metal-metal adhesive single lap, tubular, metal-metal and composite tee joints were analysed for the variable thermal and specified structural boundary conditions. The variable thermal boundary conditions cause non-uniform temperature distributions through the adhesive lap joints; consequently, non-uniform thermal strain and stress distributions occur. The adherend and adhesive regions in the neighborhood of the adhesive-adherend interfaces were subjected to high stress concentrations.

Nonlinear analysis of 3-D steel frames

Adequate mechanical properties make stainless steel an excellent construction material for structures. The current stainless steel European structural code EN1993‐1‐4 (2015) is largely based on provisions given for carbon steel EN1993‐1‐1 (2005) and does not establish specific design rules for the global analysis of stainless steel structures. Thus, the same classification criterion applies in both codes for sway and non‐sway structures, as well as providing the same predicting expressions for the amplification of bending moments in basic structures, despite the considerable differences between the mechanical behaviour of these two materials. However, recent numerical research on stainless steel frames with H cross‐sections by Walport et al. (2019) showed that the degradation of stiffness due to material nonlinearities considerably affects the response of stainless steel frames, causing greater deformations and increasing second order effects.In order to contribute to the optimal design of stainless steel structures, this paper investigates the influence of the nonlinear material response of stainless steel alloys on frame‐type structures with Rectangular Hollow Sections based on the experimental results conducted by Arrayago et al. (2019), and the interaction of material and geometric nonlinearities.

Dynamic soil–structure interaction (SSI) represents an interdisciplinary subject characterized by complex geometrical and material nonlinearities affecting both the soil and the structural components of the system under study. In the current practice, SSI problems are often solved using the so-called substructure method based on decomposing the superstructure-foundation-soil system into two subsystems whose response is determined independently. The direct method is a more general procedure to tackle SSI problems which is in principle capable of accounting for both soil and structural nonlinearities. Despite this generality, most of the current computational platforms are specialized either for structural applications or for geotechnical applications. Whereas the formers are capable to accurately reproduce the nonlinear response of the structural elements, they are usually poor in modeling soil nonlinear behaviour especially under earthquake loading. On the other hand, the latter do the reverse: they are advanced in modeling soil response but typically rough in reproducing the behaviour of the structural components of the system. Inevitably, all structures interact with the ground and therefore the need to model material and geometric nonlinearities maybe important both in the ground and structural elements. The variation of the stiffness mismatch between soil and structural elements during ground motions is one of the most influential parameters for the assessment of the kinematic component in SSI problems. The variation of the stiffness ratio is mainly governed by material nonlinearity that can develop in either the soil or the structural parts of the system. This paper presents a nonlinear constitutive model for beam elements that is compatible with performance–based earthquake engineering principles because it is capable to simulate the cyclic degradation of mechanical properties and to assess the damage suffered by the structural system. The proposed model is based on distributed plasticity and can be easily implemented in any computational platform allowing the use of an explicit solver. The article describes the theoretical aspects of the model. Validation and application of the model to the solution of a dynamic soil–structure interaction problem where the nonlinear behaviour of geomaterials is coupled with the inelasticity of structural elements, are presented in a companion paper (Andreotti and Lai in Bull Earthq Eng 2017).