Topological Microstructural Optimization. ANSYS dataset for rectangular cavities

Topological optimization software does not build a model of an object from scratch. It loads a geometric model of a product that was previously manufactured using another method. The process of building a new model is quite time consuming and requires large computational resources. This modeling method is called the finite element method. For each point of the product, the program makes and solves integral equations, taking into account the relationships between all points. The calculation results in a new geometry. The designer can then change something in the model if necessary. The end result is a CAD model. Next, for verification, the model is loaded into other software, where it undergoes a final check for maximum deformations, stresses, and so on.
The elastic medium is referred to as “matrix material” in order to distinguish it from the inhomogeneities. The role of the inhomogeneities play cavities, or voids. Several different variants of “density-based” topology optimization procedures are possible for the numerical simulation purposes. In general case, the shapes of cavities could have the arbitrary form and must not be circular or spherical. The isotropic elastic material can turn into the transversely isotropic or orthotropic material for the rectangular cavities. The rectangular voids are oriented in the directions of the coordinate axes x_1 ,x_2 . The sizes a,b of the voids in the directions of the coordinate axes x_1 ,x_2 . The inclusions are located double periodically in the chess-board order. The distances between the centers in both directions are equal respectively A,B. The representative area of material cell, which contains one rectangular cavity, and the area of the cavity are equal correspondingly to A*B. According to definition, porosity is the ratio of area of a cavity to the area of the representative area:
p≝ab/AB.
The solution determines the optimal shape of the rectangular hole for the extremal elastic energy density. The results be used for the programming of the algorithm of the topology optimization. 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.