SIMULIA Abaqus Research Articles

Improving the Impact Resistance of Anti-Ram Bollards Using Auxetic and Honeycomb Cellular Cores

Security is a crucial matter, and when it comes to road safety, barriers are increasingly needed to protect assets and pedestrians from intentional and accidental vehicular impacts. Hollow steel tubes are commonly used to produce bollards; however, their impact resistance and energy absorption are limited. Hence, the aim of this study is to investigate whether the addition of honeycomb and auxetic cellular cores can improve the energy absorption and protection level of existing bollards. Hollow bollard, a honeycomb–core bollard and an auxetic-core bollard were numerically modeled and tested (using Simulia Abaqus software, version 2019) against the impact of M1-class vehicles (of 1500 kg mass) at five different speeds (following PAS 68:2013 British standard). Hence, 15 cases/numerical models were considered, with 5 cases for each bollard type. The results revealed that the addition of an auxetic cellular core to the bollard system could increase its energy dissipation by 52% compared to the hollow steel bollard. Moreover, the proposed auxetic anti-ram bollard system was capable of stopping an M1-class vehicular impact of 64 km/h compared to only 32 km/h when using a hollow steel bollard. To the authors’ knowledge, the use of an auxetic core, explicitly for anti-ram bollards, can be considered the novel part of this research.

Использование новых видов технологической оснастки при изготовлении нежестких плоскостных алюминиевых деталей методом волновых технологий

It has been suggested that wave technologies in non-rigid plane parts production should be used with the introduction of ultrasonic range vibrations into the shaping zone in combination with technological equipment, i.e. it is- a zero-base system. The traditional technique used in domestic enterprises implies a high probability of out-of-flat conditions and deformations due to the influence of technological residual stresses (TRS) in the process of stock removal or force stresses under plastic deformation of the part when fixing blanks. Using modern universal software systems such as Simulia Abaqus, ANSYS, etc., it was possible to determine the magnitude of deformations, aligment errors caused by residual stresses. The data obtained were used to calculate rational ways for fixing some typical non-rigid plane aluminum blanks on a technological equipment - a zero-based system of German production SCHUNKVERO–SAviation (VSA). The research was aimed at determining the manufacturability for the use of such equipment when making a particular non-rigid blank made of aluminum alloys and finding the most optimal way of its fixing. The estimated values of the TRS were determined by mechanical and X-ray methods. The calculations were performed using real parts of aircraft equipment of the "beam" type and blanks made of aluminum rolled products. The proposed method for determining the maximum amount of deformation of the workpiece under machining is applicable to the most optimal placement of the support and clamping modules of the zero-based system (VSA). In combination with a certain strategy of wave mechanical processing, it makes a practically complete compensation for deformations possible and allows obtaining a suitable product from the first presentation without performing an additional correction operation.

Research of stress-strain state of the reinforcement profile during the stretching–bending–rebending (cold stretching)

The Cold Stretching method (SBR: stretching, bending with rebending), widely used abroad, makes it possible to implement low strain degrees in high-performance reinforcement production lines, increasing the level of reinforcement mechanical proprieties till A500. The process consists of a combination of stretching the reinforcement at a controlled degree of cold plastic deformation with the addition of alternating bending elements in special roller systems. The paper presents the results of computer finite element modeling in SIMULIA Abaqus complex of stress-strain state of periodic profile reinforcement in the process of SBR. The simulation results showed that during the SBR process the reinforcement receives an equivalent degree of compressive and tensile strain when passing through each subsequent roller, that is, during the transition between groups of rollers and individual rollers in a pair, each section of the profile receives a tensile load commensurate in modulus with the subsequent compression load. To verify this observation in the industrial conditions of OJSC MMK-Metiz, samples of the studied A400 reinforcement were selected in the hot-rolled state and after the SBR process. The study showed that the geometric parameters of the profile remained within normalized limits and no protrusion integrity violations were observed, which confirms the modeling results.

Application of holography method for the restoration of the Williams series near the crack tip

The article describes the processing of the results of a series of experiments performed by the interference-optical method of holographic interferometry (holographic photoelasticity) aimed at computing the amplitude coefficients of the M. Williams series constituting the stress and displacement fields at the crack tip for several cracked configurations. The main objective of this study is the experimental and computational determination of the coefficients of the M. Williams series for the stress, strain and displacement fields associated with the crack tip in an isotropic linearly elastic medium taking into account regular (non-singular) terms in the multiparameter Williams series. These coefficients are named generalized stress intensity factors. The method of holographic interferometry is shown to be a convenient and efficacious tool for reconstructing the stress field near the tip of the crack, because during the experiment it is possible to obtain two families of interference fringe patterns: absolute retardation fringes (isodromics) for vertical and horizontal polarizations. Experimental outcomes were thoroughly processed using the developed digital application allowing us to accumulate the isodromics orders and coordinates of points belonging to absolute retardations. In this work, absolute retardation fringes in a plate with a central horizontal crack and a crack inclined at different angles are obtained. For each type of experimental sample, the coefficients of the Williams series were calculated taking into account non-singular terms (in the representation of M. Williams, fifteen terms were preserved). A procedure for linearization of nonlinear algebraic equations following from the relations of Favre’s law is proposed. By solving the obtained overdeterministic system of linear algebraic equations, the generalized stress intensity factors (coefficients of the M. Williams series) are estimated. Conjointly, the finite element analysis of the specimens with same geometry was effectuated. The experimentally determined values of the Williams series are compared with the results of the finite element calculation of the stress-strain state performed in the SIMULIA Abaqus software.The results of the numerical and experimental studies were found to be quite consistent. It is lucidly shown that it is imperative to keep the higher order terms in the Williams series expansions for the fields associated with the crack tip.

Effect of damage accumulation on the asymptotic behavior of stresses ahead the crack tip

The subject of this study is the analysis of mechanical fields associated with a crack tip under creep conditions, taking into account the phenomenon of damage accumulation. The objective of the study is to perform finite element modeling, using the SIMULIA Abaqus software package, of uniaxial tension of a plate with a central horizontal crack under creep conditions, taking into account damage accumulation. For numerical simulation of creep, the Bailey-Norton power law is used. The power law of creep with the help of the user procedure UMAT (User Material) of the SIMULIA Abaqus package was supplemented with the Kachanov-Rabotnov kinetic equation of damage accumulation in a related formulation. In the calculation scheme of finite elements, the crack tip was modeled as a mathematical notch and as a notch with a finite radius of curvature. As a result of the calculations, the distributions of stresses, strains, and continuity under creep conditions were obtained, taking into account the accumulation of damage over time. Radial distributions of continuity, stresses, and strains are plotted over time at various distances from the crack tip. The subject of the study was the consideration of the asymptotic of the stress distribution. As a result of the study, it is shown that in the elastic region the asymptotic corresponds to the distribution under the elastic regime, and in the creep zone the asymptotics of Hutchinson, Rice and Rosengren (HRR-solution) is satisfied for different exponents nof the power law of creep.
 A comparison is made of the radial stress distributions in modeling without taking into account damage and in the case of taking into account damage accumulation. It is shown that the presence of damage significantly changes the asymptotics of the stress field in the vicinity of the crack tip.

LOW-CYCLE FATIGUE OF STRUCTURES WITH STRESS CONCENTRATORS

The results of experimental and theoretical studies of structures with stress concentrators under cyclic loads are presented. The studies were carried out on cylindrical samples with a V-shaped annular recess under mild cyclic loading. The tests were carried out on samples of the BrH08-Sh alloy with a cyclic change in the tensile load from 0 to 10.8 kN. Under such loading, the material in the recess area undergoes cyclic elastoplastic deformation, which leads to destruction as a result of low-cycle fatigue. For mathematical modeling of the elastic-plastic behavior and destruction of structures with stress concentrators, a variant of the theory of plasticity based on the theory of flow under combined hardening is used. In the chosen plasticity model, a memory surface is introduced that separates the processes of monotonous and cyclic loading. This separation makes it possible to take into account various features of isotropic and anisotropic hardening of the material. Anisotropic hardening is represented as a sum of microstresses of three different types, which make it possible to describe the effects of landing and stepping of the elastic-plastic hysteresis loop. The plasticity model makes it possible to assess the damaged state of a material based on the kinetic equation of damage accumulation based on the energy principle (the operation of microstresses in the field of plastic deformations). The material behavior model is embedded in the finite element software package SIMULIA Abaqus. The results of calculations and experiments on the magnitude of axial deformation, the average axial deformation on the surface of the recess and the number of cycles to failure are compared. It is found that in a design with a recess with a radius of 1 mm, a soft asymmetric loading with a unilateral accumulation of deformation (ratcheting) is realized in the concentration zone.

The effect of an explosive shock wave on the plate of a protective structure of a critical infrastructure

The article presents the outcomes of an analysis on the stress-strain conditions of reinforced concrete structures subjected to an explosive shock wave resulting from the detonation of a combat unit from a kamikaze drone against a protective screen. When designing protective structures for critical infrastructure, employing computer simulation enables an assessment of the genuine impact of explosive loading on the structural elements' strength. The active phase of explosive loading is exceptionally brief, lasting only a fraction of a second. Under such circumstances, modeling is best performed using explicit methods of direct integration in time.
 The structure considered in this work is a reinforced concrete slab supported by a metal beam cage with I-beam cross-sections, topped with a sand backfill. The study was executed within the SIMULIA Abaqus software suite, incorporating models depicting nonlinear material behavior in a three-dimensional context. Discretely positioned reinforcement was considered for reinforced concrete structures, and the "Concrete Damage Plasticity" model was applied for concrete, accounting for damage accumulation. The devised computational scheme for the shelter represents a section of the protective structure's roof under conditions of cyclic symmetry.
 The article elucidates the core principles of incorporating explosive loading according to algorithm CONWEP.The results demonstrate that during the detonation of a kamikaze drone, an explosive wave created a crater in the sand backfill, exposing the slab. The study illustrates the development of damage in the reinforced concrete slab at various time intervals. Despite the identified damage to the slab, the protective structure overall withstood the explosive load. The intensity of the explosive shock wave diminishes significantly as it propagates away from the explosion site.

Modern software features for shape optimization of shells

Shape optimization, as one of the types of structural optimization problems, is an important process in the design of shells, since it contributes to the creation of a structure with fine performance characteristics, expansion of design variations and knowledge base to obtain high-quality results. To solve the problems associated with determining the shape and creating more advanced structures, software packages include a special optimization module, which can be based on one or more mathematical methods, the purpose of which is to provide the best solution in the shortest possible time. The research is focused on the process of shape optimization in three well-known universal software packages: Ansys Mechanical, COMSOL Multiphysics and Simulia Abaqus, as well as in Rhinoceros modeling software with a special visual Grasshopper plugin. The purpose of the study is to analyze the technology of shape optimization in four software packages and to compare them with each other in terms of the problem-solving process, user interface, the fullness of libraries, accessibility for educational purposes and system requirements for a computer. The authors specify and describe the characteristic features of each software package. It was found that all the software packages under consideration are equipped with great opportunities for shape optimization of structures and have a variety of functionality for solving this type of tasks. The development of optimization technology in calculation and modeling software packages will allow obtaining the most effective solutions in the process of designing shells of complex shapes.

Modeling of Stochastic Material Properties with User Subroutines in SIMULIA Abaqus

This article describes a software module component integrated with the SIMULIA Abaqus engineering analysis software package and designed to simulate random values of material parameters in a finite element model based on specified statistical characteristics, with the possibility of taking into account the physical nonlinearity of material behavior under various combinations of loads and influences. The target group of materials under study is materials of load-bearing elements of building structures, such as concrete, stone, steel. This software module can be recommended for use by specialists, engineers and scientists engaged in probabilistic analysis of the reliability of structures of buildings and structures, apparatus, machines, devices, with the combined use of complexes of computer modeling and engineering analysis. Has a certificate of state registration of the computer program «AS for modeling stochastic properties of materials» No. 2019667439 dated 12.24.2019.

Combined experimental–numerical mode I fracture characterization of the pultruded composite bars

In this paper, pultruded GFRP bars are investigated to determine their fracture properties. The double cantilever beam test (DCB) is used to assess fracture behavior under mode I loading conditions. However, due to the presence of the R-curve effect (variable fracture energy dependent on the length of the crack), it is necessary to introduce a nonstandard approach to determine fracture properties. The mixed experimental–numerical approach is proposed to deal with this issue. Numerical simulations were carried out in Simulia Abaqus, and with Python scripting it was possible to generate models and obtain R-curve for the material. The numerical model built based on the experimental results has very good agreement with it (force–displacement and delamination length–time characteristics) which allows the use of the mentioned model in the analysis of more complex structures. Acoustic emission analysis was introduced as an auxiliary technique. The delamination obtained from both the numerical model and the experiment complies with the registered acoustic emission events. The proposed method can be used in preparing a material model for other composite materials, which display the presence of the R-curve effect.

ASYMMETRIC DISTRIBUTION OF PIPE ADAPTER FOR CARS

It is shown that the responsible parts of each vehicle are tubular connecting lines, which are included into the braking, fuel and exhaust systems of cars. These pipelines have high requirements for reliability, vibration resistance, strength, corrosion resistance and durability. These parts are used as expanders and connecting elements when transitioning from a smaller pipeline diameter to a larger one. The paper presents studies of the operation of distributing the end of the pipe blank with a rigid punch. In the process of distribution, the acting tangential stresses lead to a decrease in the thickness of the edge section of the workpiece. This entails a decrease in the reliability of this area during operation and a decrease in its maintainability and corrosion resistance. Also, to ensure the tightness of pipe connections, threads are cut or these areas are welded together in the specified areas of the workpieces. Therefore, an important design feature of tubular diffusers is the same wall thickness throughout the cross-section of the semi-finished product. To solve the problem of increasing the thickness of the semi-finished product after distribution, an asymmetric tool is proposed. The task was solved in the finite-element formulation using a special complex of 3D modeling Simulia Abaqus – student edition. The pipe blank was represented as a deformable solid, while the punch was modeled as a completely rigid discrete solid. The construction method for both models is "revolution". According to finite element modeling, dispensing with a conical asymmetric tool has advantages from the point of view of increasing the thickness of the end zone of the pipe bell. The thickness of the part increases by 22.5% from a thickness of 1.77 mm for the classic version of distribution, to 1.82 mm – for distribution with an asymmetric tool. To reduce the thinning of the wall after distributing the pipe blank, it is recommended to use an asymmetric punch. To obtain a symmetrical pipe socket, it is necessary to make two dispensing transitions with a 180° rotation of the blank or punch

To the scrutiny of the experiential and computational elicitation of factors of the Williams multi-parameter expansion

The article defines stress fields near the tips of mathematical cracks in an isotropic linearly elastic plate with two horizontal collinear cracks lying on a straight line of different lengths under the uniaxial tensile condition, using two approaches - experimental, based on the method of digital photomechanics, and numerical, based on finite element calculations. To represent the stress field at the tip of the section, the Williams polynomial series is used - the canonical representation of the field at the top of the mathematical section of a two-dimensional problem of elasticity theory for isotropic media. The main idea of the current study is to take into consideration the regular (non-singular) terms of the series and analyze their impact on the holistic description of the stress field in the immediate vicinity of the top of the section. The first fifteen coefficients of the Max Williams series were preserved and determined in accordance with experimental patterns of isochromatic bands and finite element modeling. To extract the coefficients of the Williams series used a redefined method designed to solve systems of algebraic equations, the number of which is significantly greater than the unknown - amplitude multipliers. The influence of the non-singular terms of the Williams series on the processing of the experimental pattern of interference fringes is demonstrated. It is validated that the preservation of the terms of a high order of smallness makes it possible to expand the area adjacent to the tip of the crack, from which experimental points can be selected. The finite element study was carried out in the SIMULIA Abaqus engineering analysis system, in which experimental samples tested in a full-scale experiment were reproduced. It is revealed that the results obtained by the two methods are in good agreement with each other.

Numerical analysis of a steel frame in a fire situation

In the paper, the stages of modelling of a steel frame under fire conditions were discussed. Numerical computations were performed using SIMULIA Abaqus software. The way of defining and developing the computational model was described. In the numerical procedure adopted in the paper, much attention was paid to formulas related to various types of the model parameters that depend on the fire temperature. The results were shown in a graphic form. They were compared with the results obtained from the analysis, in which the impact of elevated temperatures was disregarded. Based on numerical simulation results, an attempt was made to assess the effect of fire on the steel frame components. The paper is exploratory in character and provides an introduction to the issues related to the modelling of steel structure fires. The numerical modelling of the structure fire described in the paper can have practical potential for structural engineers.

Low-cycle fatigue of V-notched cylindrical samples of bronze alloy

The article presents the results of experiments on cyclic loading of samples with an annular V-shaped notch and their mathematical modeling. The tests were carried out on specimens of the BrKh08-Sh alloy with a cyclic change in the tensile load from 0 to a given value. Under such loading, the material in the groove area is subjected to cyclic elastoplastic deformation, which leads to failure due to low-cycle fatigue. When testing samples using the digital image correlation method, the deformation of the material on the surface of the undercut was measured, which made it possible to determine the nature of the change in its range from cycle to cycle. Mathematical modeling of experiments is carried out according to the finite element method. For this purpose, models of elastic-plastic deformation and accumulation of material damages are introduced into the SIMULIA Abaqus software package. The plasticity model is based on the theory of flow under combined hardening. The damage accumulation model is based on the energy strength criterion. The article presents the basic equations used to calculate the models. The material parameters are determined and verified based on the results of a basic experiment on cyclic tension-compression of a smooth cylindrical sample under asymmetric rigid loading. Based on the results of the calculation, cartograms of stresses, deformations, and accumulated damages were constructed. It is shown that when the sample is unloaded, in the area of stress concentration close to the annular groove, compressive stresses arise, the values of which are close to the values of tensile stresses at the moment of application of the maximum load. The results of mathematical modeling are compared with the experiment. A comparison of the results was carried out in terms of the range of axial deformation of the material on the surface of the undercut and the number of cycles before failure.

APPLICATION OF THE UMAT SUBROUTINE FOR SOLVING CONTINUUM MECHANICS PROBLEMS (OVERVIEW)

This paper presents an overview of the application of the UMAT subroutine of the SIMULIA Abaqus multifunctional software package in solid mechanics and related areas. This subroutine is used to describe new user materials that are not available in the class of standard materials of the SIMULIA Abaqus package. This overview article provides examples of problems and constitutive equations of materials that are modeled using UMAT / VUMAT procedures. Various types of materials are presented, successfully described by means of user-defined UMAT and VUMAT procedures. A general description and experience of using the UMAT subroutine is given. The results of finite element modeling of the deformation of aplate weakened by a central circular hole under uniform and uniaxial tension with steady-state creep in a damaged medium evolving according to a power law are presented in the coupled formulation of the problem (creep - damage). The distributions of stresses, strains, and damage fields at the tip of the defect under creep conditions are found, and an analysis is made of the effect of the damage accumulation process on the stress fields at the crack tip under steady-state creep conditions. The distributions of stresses and creep strains are demonstrated taking into account the accumulation of damage over time.

Buckling of cylindrical concrete tanks and silos due to prestressing — nonlinear approach

The buckling of concrete cylindrical tanks and silos is associated mainly with prestressing, which influences the meridional critical force. Higher compression produces a lower meridional critical force. For three-dimensional structures subjected to biaxial or triaxial loading, the simplified methods of stability analysis proposed in Eurocode standard for concrete structures are inappropriate. The authors try to answer which procedure may be helpful for the assessment of buckling possibility, which results from prestressing of cylindrical structures. The numerical analyses are performed with the use of “Simulia Abaqus system”, which allows the nonlinear stability analysis adopting the plasticity-based damage material model and assuming initial imperfections. Two variants of load distribution (constant and hydrostatic external prestress) and two variants of wall-foundation connection are considered. The results are presented with the use of two parameters. The first one constitutes the ratio of lateral pressure to vertical pressure on the upper edge. The second one describes the ratio of current vertical force – corresponding to real load – to the initial test value of the iterative process. The obtained relationships of critical vertical force and the level of external prestress for cylindrical tank of height twice the diameter can be the guideline for engineers in designing process.

Developing A Needle-Knife Surgical Device

Scope Nowadays, a new era of orthopedic surgery is taking place. Procedures like ultrasound-guided interventions, invasive pain orthopaedics interventions, started to be widely performed. Objective The aim of the project is a virtual development of a needle-knife surgical device to be useful for minimally invasive orthopaedic surgical procedures and other surgical procedures. Method Three different needle devices were compared. One is a base model 1 and the other two are experimental models 2 and 3. They are based on a metal guide for intravenous catheter 14Gx2’’. The base one model 1 is the metal guide for intravenous catheter 14Gx2’’; the experimental model 2 is a flat beveled edge, and experimental model 3 is a board bevel Edge. They are all graduated, parylene-coated, with a stop handle needle guard. The devices were developed by 3D Design 3D STEP Standard Format, Catia V5 Format, and 2D Format Design and 3D Model. They were biomechanically simulated with Virtual Biomechanical Strength Simulation (Software Simulia Abaqus).. The Strengths were assessed by Needle Strength Analysis (CAE Simulation). Results: The present study compares three models. A control base model 1 and two experimental models; model 2 and model 3. Model 3 presented similar features in rigidity to the baseline model 1 (3,6%). They have a similar performance. The tip of model 3 increased a tension of 15%; but does not mean fracture risk 22. S Conclusion: These devices seem suitable for eco assisted orthopaedic surgery interventions and other procedures according to virtual analisis. Further in vivo procedures must be performed.

Effect of microstructure on trabecular-bone fracture: numerical analysis

Trabecular bone tissue with its complicated microstructural morphology can exhibit complex and random fracture patterns. This paper focuses on the effect of morphology of bone tissue on processes of its deformation and fracture. For this purpose, three-dimensional unit cells of trabecular bone tissue were generated based on the scans of human distal tibial bone obtained with high-resolution peripheral quantitative computed tomography (HR-pQCT). Mechanical behavior of porous structure of trabecular bone was investigated under conditions of applied tensile and compressive loads employing a model of degradation of elastic properties, numerically implemented with finite-element analysis. The calculations were performed in Simulia Abaqus using the UMAT custom subroutine.

МАЛОЦИКЛОВАЯ УСТАЛОСТЬ ОБРАЗЦОВ С КОЛЬЦЕВОЙ ВЫТОЧКОЙ ПРИ ЖЕСТКОМ НАГРУЖЕНИИ

The results of tests of cylindrical specimens of alloy 01570C for low-cycle fatigue are presented. The tests were carried out on a smooth sample and samples with an annular recess. Specimens with an annular groove were tested under rigid cyclic alternating loading with a constant range of elongation of the working part. To simulate the experiments performed, a variant of the plasticity model based on the theory of flow under combined hardening is used. In the chosen mathematical model, a memory surface is introduced that separates monotonous and cyclic loading. This division allows one to take into account various features of isotropic and anisotropic hardening of the material. Anisotropic hardening is described by the sum of backstresses of three different types, which make it possible to describe the effects of fitting and stepping out of the elastoplastic hysteresis loop. The plasticity model makes it possible to assess the damaged state of a material using an equation that describes the process of damage accumulation based on the energy criterion of durability. According to the results of testing a smooth sample, the parameters of the plasticity model were determined. The finite element method was used to carry out mathematical modeling of experiments on loading samples with an annular groove. The material behavior model was implemented in the SIMULIA Abaqus software package, for which the model equations were linearized and the Jacobi matrix was calculated, which determines the change in each of the stress increment components caused by an infinitesimal change in each component of the strain increment tensor. Based on the results of mathematical modeling, the dependences of the load applied to the sample on the elongation of its working part were obtained. The article compares the dependences of the load applied to the sample, obtained from the results of the calculation, with the experimental ones, as well as the number of cycles until the destruction of the sample.

Topology optimization of an oil tanker bulkhead subjected to hydrostatic loads

In the field of Naval Architecture, the conventional approach to design any vessel is to follow the classification societies’ rules to ensure adequate strength and structural integrity. Nowadays, owners’ demands and purposes of vessels are changing dramatically. To mitigate these demands, sometimes it is necessary to design new types of structures, but the classification society’s rules are not sufficient to prepare these advanced designs. Moreover, Naval Architects are always eager to minimize the lightweight of a vessel as this is directly related to cost and carrying capacity. Topology optimization has become a powerful tool for designing structures in an optimized way. The concept of topology optimization has been utilized by the automotive and aerospace industry for almost thirty years where problems associated with solutions meant to satisfy maximum stiffness and structural integrity with minimum weight which are of utmost importance. However, in the field of marine and offshore structures, the use of topology optimization is infrequent. As structural optimization aims to design structures under certain constraints to achieve better strength and lower cost, the introduction of this technique in ship structure can be lucrative. In this paper, a methodology to apply structural topology optimization in the field of ship design is presented. An Oil Tanker Bulkhead has been selected for this study. SIMULIA ABAQUS software is used in this regard. Topology optimization has been performed by minimizing the strain energy of the component as the objective function and a target stiffness and material volume of the structure as design constraints. Finally, the results demonstrate the general applicability of the methodology presented for obtaining the geometrical layout of the structure.