SIMP type topology optimization procedure considering uncertain load position

In this paper a new type of probabilistic optimal topology design method is elaborated for continuum type of structures where the points of application of the loads are given randomly. In the proposed probabilistic topology optimization method the minimum penalized weight design of the discretized structure is subjected to compliance constraint and side constraints. The compliance expression is probabilistic one. By the use of an appropriate stochastic upperbound theorem, the original stochastic mathematical programming problem is substituted by a deterministic one. The numerical procedure is based on iterative formula which is formed by the use of the first order optimality condition of the Lagrangian function. The application is illustrated by numerical example

APPLICATION OF INTERNAL VARIABLES IN CASE OF TIME-DEPENDENT LOADING FOR ANALYSIS OF STRUCTURES WITH DAMPING

A new approach is presented for the analysis of structures with time-dependent loading based on mathematical programming in the function space L2. The solution occurred in the vector space. In this paper the computational model of the structures with damping is detailed by the use of internal variables. The energy dissipation is taken into account. A comparison between the conventional and this new model can be read

NONLINEAR ANALYSIS OF PLANE PROBLEMS BY MATHEMATICAL PROGRAMMING

A mixed variational principle based on a bilinear material model and on complementary potential energy is applied to the analysis of plane problems. Two discrete models are used to the construction of the fundamental equations. The first model consists of rigid rectangular panels connected along the edges by springs acting in tension, compression and shear and the other one is based on the standard finite element method. The application is illustrated by the solution of a numerical example

Optimal design of curved folded plates

The plated structures are one of the most frequently used engineering, structures. The object of this research work is the optimal design of curved folded plates. This work is an ongoing investigation. There are various solution methods to analyze this type of structures. Here the finite strip method is used. At first single load condition is considered, but later the multiple load conditions are used for the design. The base formulation is a minimum volume design with displacement constraint what is represented by the compliance. For the multiple loading two equivalent topology optimization algorithms can be elaborated: minimization of the maximum strain energy with respect to a given volume or minimization of the volume of the structure subjected to displacement constraints. The numerical procedures are based on iterative formulas which is formed by the use of the first order optimality condition of the Lagrangian-functions. The application is illustrated by numerical examples

TIME-DEPENDENT STRESS-LIMITED MECHANICAL MODELS OF ELASTO-PLASTIC PROCESSES

In generall, the mechanical models are described by different type of differential equations. In the approach presented here the unconstrained optimization problem that derives from the boundary problem is decomposed into a pair of constrained optimization problems. In this paper the presented models concerning the stress-limited elasto-plastic state change include the theoretical results of the earlier studies. The theoretical results are illustrated by some numerical examples

Parametric Study on the Element Size Effect for Optimal Topologies

Topology optimization is complex engineering design tool. It needs intensive mathematical, mechanical and computing tools to perform the required design. During its hundred years of history it has become clear that the non-unique solution property of the method is affected by the material parameters (Poisson ratio) and the ways of the discretization. The aim of the paper is to investigate the influence of parameter changes to optimal design property in tasks with great number of degrees of freedom. The parametric study includes influence of material parameter (Poisson ratio) as well as the size of the ground elements which are commonly applied during the discretization. Increasing the size of the ground elements while the total number of the finite elements is constant, the computational time is significantly reduced. Therefore the study on changing accuracy versus ground element resolution may be important factor in choosing ground element size. In addition to it the effective properties of arrangements of the strong and weak materials (black and white elements) in a checkerboard fashion are also investigated. The Michell-type problem is investigated by the minimization of the weight of the structure subjected to a compliance constraint

Modal Approximation Based Optimal Design of Dynamically Loaded Plastic Structures

The purpose of this study is to present an optimal design procedure for elasto-plastic structures subjected to impact loading. The proposed method is based on mode approximation of the displacement field and assumption of constant acceleration of impacted structure during whole time of deformation process until the plastic displacement limit is reached. Derivation of the method begins with the application of the principle of conservation of linear momentum, followed by determination of inertial forces. The final stage of the method utilizes an optimization technique in order to find a minimum weight structure. Eventually, effectiveness and usefulness of the proposed method is demonstrated on the example of a planar truss structure subjected to dynamic loading caused by a mass impacting the structure with a given initial velocity

Stochastic compliance constrained topology optimization based on optimality critera method

The aim of this research is to introduce a new type of stochastic optimal topology design method with iterative solution technique. The paper presents stochastic topology design procedure and compares the achieved results with optimal obtained topologies on deterministic way. The standard mathematical programming problem is based on a minimum volume design procedure subjected to a bounded compliance constraint given in stochastic form. In the numerical method an optimality criteria procedure is used

Rugalmas-képlékeny tartószerkezetek topológiai optimalizálásának néhány különleges feladata = Some particular problems of topology optimization of elasto-plastic structures

Módszereket dolgoztunk ki normál és rendkívüli (robbanás, ütés és földrengés) terhekkel terhelt rugalmas képlékeny tartószerkezetek optimális tervezésére. A rugalmas feszültségekre és a képlékeny alakváltozásokra korlátokat vezettünk be. A földrengés vizsgálat az EUROCODE 8 által javasolt Pushover módszerre alapszik. A topológia optimálás területén a tovább fejlesztett SIMP módszert sikeresen alkalmaztuk. Több, új típusú Michell-feladat vizsgálata is megtörtént. A többcélfüggvényes matematikai programozást felhasználva megoldottuk a korlátozott alakváltozási képességű, rendkívüli dinamikus terhelésű rugalmas-képlékeny szerkezetek optimális tervezését. Egyidejűleg két célfüggvényt, a tartószerkezet súlyát és a maradó elmozdulást vesszük számításba. Kezdeti eredményeket értünk el a képlékeny-lágyuló és laza-záruló anyagú tartószerkezetek optimális tervezése terén. Az optimálási feladat itt nem-konvex, így az optimumot egymásba ágyazott két ciklussal kaptuk meg. Az időben változó, kvázi-statikus terhelésű rugalmas-képlékeny anyagú tartószerkezetek képlékeny határállapot alapján való optimális tervezésére új számítási eljárást készítettünk, amely figyelembe tudja venni a disszipációt is. Az általunk készített módszer és a klasszikus képlékenységtanból ismert tervezési eljárás kapcsolatát is vizsgáltuk.Számítógépes programokat fejlesztettünk ki és mintafeladatokon teszteltük azokat. | Methods were developed to the optimal design of elasto-plastic structures subjected to normal and extreme (explosion, impact, earthquake) loads. Constraints were applied to the elastic stresses and plastic deformations. The earthquake analysis was based on Pushover method suggested by EUROCODE 8. The plastic displacements were controlled. An iterative algorithm based on the optimality conditions of mathematical programming was elaborated to layout optimization. The successful application of the SIMP method made possible the use of a great number of variables which promotes significantly the solution of engineering problems. Several Michell-type topologies were investigated. A solution method was elaborated for the optimal design of structures subjected to time dependent, quasi-static loading. The relation with the classical optimal solution was studied. A design model was presented for the layout optimization of elasto-plastic structures subjected to dynamic loading by the use of multicriteria optimization. The objective functions were: the weigth and the permanent deformations.The limit analysis of structures was investigated by the use of nonlinear softening material. The non-convexity of the problem did not cause any difficulties because of the use of nested loop. At each problem computer programs were developed and applied to the solution of test examples

Structural Topology Optimization with Stress Constraint Considering Loading Uncertainties

This paper deals with the consideration of loading uncertainties in topology optimization via a fundamental optimization problem setting. Variability of loading in engineering design is realized e.g. in the action of various load combinations. In this study this phenomenon is modelled by the application of two mutually excluding (i.e. alternating) forces such that the magnitudes and directions are varied parametrically in a range. The optimization problem is stated as to find the minimum volume (i.e. the minimum weight) load-bearing elastic truss structure that transfers such loads acting at a fix point of application to a given line of support provided that stress limits are set. The aim of this paper is to numerically determine the layout, size, and volume of the optimal truss and to support the numerical results by appropriate analytical derivations. We also show that the optimum solution is non-unique, which aects the static determinacy of the structure as well. In this paper we also create a truss-like structure with rigid connections based on the results of the truss optimization and analyse it both as a bar structure (frame model) and a planar continuum (disk) structure to compare with the truss model. The comparative investigation assesses the validity of computational models and proves that the choice aects design negatively since rigidity of connections resulted by usual construction technologies involve extra stresses leading to significant undersizing