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

Reliability based design of frames with limited residual strain energy capacity

The aim of this paper is to create new type of plastic limit design procedures where the influence of the limited load carrying capacity of the beam-to-column connections of elasto-plastic steel (or composite) frames under multi-parameter static loading and probabilistically given conditions are taken into consideration. In addition to the plastic limit design to control the plastic behaviour of the structure, bound on the complementary strain energy of the residual forces is also applied. If the design uncertainties (manufacturing, strength, geometrical) are taken into consideration at the computation of the complementary strain energy of the residual forces the reliability based extended plastic limit design problems can be formed. Two numerical procedures are elaborated. The formulations of the problems yield to nonlinear mathematical programming which are solved by the use of sequential quadratic algorithm