Some aspects of the genesis of structures

Abstract

BendsOe and Kikuchi (1988) introduced a novel approach of distributing mass within a specified design domain utilizing a stiffness-density relation obtained by homogenization of a cellular microstructure. This approach was extended to multiple loading cases and three-dimensional applications by the author and his associates (Mlejnek and Schirrmacher 1989;Mlejnek 1990). Moreover the well-known concept of explicit convex behaviour approximation together with a dual solution scheme (Fleury and Smaoui 1988) was successfully introduced to this problem. Further objectives such as eigenvaiues and displacements generalized the range of application. It is the aim of this paper, to develop a simplified procedure that can be easily integrated into a FEM-anaiysis package. Its application requires essentially not much more than the usual FEM-technology. Nevertheless a traceable mathematical base is still maintained. A series of examples demonstrates the suitability of this approach to the preliminary design of minimal compliance structures made of isotropic materials.

Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework

“…For example, in the well-established artificial density with penalization approach [6][7][8], the design domain is first discretized into finite elements (pixels) with reasonable resolution, then mathematical programming or optimality criteria-based algorithms are applied to find the element-wise black-and-white (i.e., 0 or 1 in each pixel) density distribution, which represents the topology of the structure, see Fig. 1 for reference.…”

Backbone cup – a structure design competition based on topology optimization and 3D printing

“…The latter researches proposed the solid isotropic material with penalization (SIMP) method [3][4][5] which made it possible to gain practical structure design through topology optimization, the ESO method [6], and the level set method [7], etc. For recent advances of topology optimization, the readers are referred to the literature surveys of Deaton and Grandhi [8], Guo and Cheng [9].…”

Length scale and manufacturability in density-based topology optimization

“…Later, the so-called SIMP (Simplified Isotropic Material with Penalization) [17] approach has been introduced in order to reduce the complexity of the original homogenization formulation. The SIMP formulation has been utilized in many following papers to improve convergence to 0/1 solution, e.g., [167] and [107], and physical justification is presented later in [19]. For linear elasticity, SIMP relates the modulus of elasticity E (x) , x ∈ Ω and the material density field by the power law given as…”