Comparative Study of Peridynamics and Finite Element Method for Practical Modeling of Defects Cracks in Topology Optimization

Recently, topology optimization of structures with cracks becomes an important topic for avoiding manufacturing defects at the design stage. This paper presents a comprehensive comparative study of peridynamics-based topology optimization method (PD-TO) and classical finite element topology optimization approach (FEM-TO) for designing lightweight structures with/without cracks. Peridynamics (PD) is a robust and accurate non-local theory that can overcome various difficulties of classical continuum mechanics for dealing with crack modeling and its propagation analysis. To implement the PD-TO in this study, bond-based approach is coupled with optimality criteria method. This methodology is applicable to topology optimization of structures with any symmetric/asymmetric distribution of cracks under general boundary conditions. For comparison, optimality criteria approach is also employed in the FEM-TO process, and then topology optimization of four different structures with/without cracks are investigated. After that, strain energy and displacement results are compared between PD-TO and FEM-TO methods. For design domain without cracks, it is observed that PD and FEM algorithms provide very close optimum topologies with a negligibly small percent difference in the results. After this validation step, each case study is solved by integrating the cracks in the design domain as well. According to the simulation results, PD-TO always provides a lower strain energy than FEM-TO for optimum topology of cracked structures. In addition, the PD-TO methodology ensures a better design of stiffer supports in the areas of cracks as compared to FEM-TO. Furthermore, in the final case study, an intended crack with a symmetrically designed size and location is embedded in the design domain to minimize the strain energy of optimum topology through PD-TO analysis. It is demonstrated that hot-spot strain/stress regions of the pristine structure are the most effective areas to locate the designed cracks for effective redistribution of strain/stress during topology optimization.

Outrigger and Belt-Truss System Design for High-Rise Buildings: A Comprehensive Review Part II—Guideline for Optimum Topology and Size Design

This article is the second part of the series of the comprehensive review which is related to the outrigger and belt-truss system design for tall buildings. In this part, by presenting and analyzing as much relevant excellent resources as possible, a guideline for optimum topology and size design of the outrigger system is provided. This guideline will give an explanation and description for the used theories, assumptions, concepts, and methods in the reviewed articles for optimum topology and size design. Finally, this part ended up with a summary for the findings of the reviewed studies, which is useful to understand how different parameters influence the optimum topology and size design of a tall building with outrigger and belt-truss system.

Periodic structures stiffness topology optimization

Stiffness topology optimization aims to determine the best material arrangement, capable of conciliating high structural stiffness and low weight, which handles certain loading conditions subjected to predefined boundary conditions. The imposed periodic constrain is fundamented on the fact that structures made of periodic materials behave as a homogeneous continuum, because the macro-structure cells are modeled as a uniform medium composed by periodic material. The optimization algorithm used in this work is the BESO (Bi-directional Evolutionary Structural Optimization), which analyzes the structure, under its loadings and boundary conditions, and generates the optimum topology through addition and removal of material. However, in order to reduce the high computational costs of this method when applied to very refined meshes, which is the case with most periodic structures, emphasis was placed on the integration between Matlab and Ansys softwares, with promising results.

Effect of Higher Order Element on Numerical Instability in Topological Optimization of Linear Static Loading Structure

This paper presents the mathematical model to solve the topological optimization problem. Effect of higher order element on the optimum topology of the isotropic structure has been studied by using 8-node elements which help in decreasing the numerical instability due to checkerboarding problem in the final topologies obtained. The algorithms are investigated on a number of two-dimensional benchmark problems. MATLAB code has been developed for different numerical two dimensional linear isotropic structure and SIMP approach is applied. Models are discretized using linear quadratic 4-node and 8-node elements and optimal criteria method is used in the numerical scheme. Checkerboarding instability in the final topology is greatly reduces when incorporated 8-node element instead of 4-node element which can be confirmed through comparing the final topologies of the structure.

Concurrent Topology Optimization of Lightweight Cellular Materials and Structures

In this paper, a two-stage optimization algorithm is proposed to simultaneously achieve the optimum structure and microstructure of lightweight cellular materials. Microstructure is assumed being uniform in macro-scale to meet manufacturing requirements. Furthermore, to reduce the computation cost, the design process is divided into two stages, which are concurrent design and material design. In the first stage, macro density and modulus matrix of cellular material are used both as design variables. Then, the optimum topology of macro-structure and modulus matrix of cellular materials will be obtained under this configuration. In the second stage, topology optimization technology is used to achieve a micro-structure of cellular material which is corresponded with the optimum modulus matrix in the earlier concurrent design stage. Moreover, the effectiveness of the present design methodology and optimization scheme is then demonstrated through numerical example.