Topological Microstructural Optimization. ANSYS dataset for 3d finite-element models
Description
In the present dataset, the elastic models of shape and topology optimization with the continuous distribution of microscopic inhomogeneities or voids in 3D-problems are presented. The topology uses the optimization method with the “topology density” approach, which applies the continuous design variables. The cloud of an infinite number of infinitesimally small voids or other inhomogeneities are used to model the medium with the variable elastic modules. The density of the inhomogeneities with the scalar or tensorial porosity functions. Chapter 9 explains the easiest implementation of the density-based methods if topology optimization into 3D models. The modelling requires the relations of the elastic properties of the materials upon the cavity, or generally, inhomogeneity content. In other words, the expressions of the effective moduli upon densities of phases are necessary. There are several possibilities to establish such expressions. The simplest method ignores the interaction of the microscopical inhomogeneities, assuming the centers of the voids are stochastically dispersed in space. For the optimal orientation, all microscopical inhomogeneities have to be identically oriented. The last condition follows from the coaxiality of stress and strain tensors in the medium with similarly oriented inclusions. In this section the body made of the periodically arranged cuboidal cells with the inhomogeneities is studied. The body extends infinitely in three dimensions. The average stresses in the plate are σ_11 , σ_22 , σ_33 . The principal stresses are parallel to the directions of coordinate axes. The inclusions in primitive cells are located tri-periodically in space. The rectangular cuboid cavities are oriented in the directions of the coordinate axes x_1,x_2,x_3. The dimensions of a rectangular cuboidal void are a,b and c, then its volume is δV=abc. The sizes A,B,C are sizes of the primitive cell in the directions of the coordinate axes x_1 ,x_2 ,x_3 respectively. The volume of the primitive cell is V. The porosity is equal to ratio of volume of the void δV to the volume of unit cell V= A B C: p≝δV/V=(a b c)/(A B C). The model describes the elastic behavior for the high grads of porosity, 0≪p<1. The matrix material volume content is: d=1-p. The elastic moduli in are programmed in the attached finite-element APDL script. The optimization is performed with the sequential algorithm.
Files
Steps to reproduce
For the illustration of the technique, the optimization was performed with the commercial finite-element program. For the simulation was chosen the proprietary finite-element system ANSYS 2023. The program ANSYS 2022 is required. The APDL script "ATOPO3D-9.txt" reads the auxiliary mesh generation file "MESH3D186.txt". The attached file requires very moderate memory and the number of elements is small enough to run the "Student version" of the commercial program ANSYS. The user can replace the mesh generation file to run the optimization script over the arbitrary 3-dimensional mesh. The MAPLE script "READ_ANSYS_DATA_3d7-3d.mw" uses the commercial CAS software to read the results form the ANSYS optput data stream.