On topology optimization of plates with prestress

In this work, topology optimization is used to optimize the compliance or eigenvalues of prestressed plates. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress stiffness matrix to the original stiffness matrix. The calculation of the sensitivities is complicated because of the initial stress stiffness matrix, but the computational cost can be kept low by using the adjoint method. The topology optimization problem is solved using the solid isotropic material with penalization (SIMP) method in combination with method of moving asymptotes (MMA). Numerical examples of minimizing compliance or maximizing the first eigenvalue of plates are given. One example is a micro electro mechanical systems (MEMS) application involving a backplate used in a microphone in a hearing aid. Copyright © 2001 John Wiley & Sons, Ltd.

This paper discusses the design of axisymmetric structures with self-supporting features that can be additively manufactured without requiring internal support structures. This is motivated by wire-fed additive manufacturing processes, many of which can fabricate designs with enclosed pores that inherently exist in many axisymmetric structures, such as double walled pressure vessels. Although enclosed pores are possible, features that rise at shallow angles from the build plate typically cannot be fabricated without the use of support structures, which require removal and thus are unfavorable in such applications. In this paper, an overhang constraint is applied to ensure that all designed features rise at a designer-prescribed self-supporting angle to eliminate the need for such support structures. This is achieved by coupling the projection-based overhang constraint approach with topology optimization and axisymmetric finite elements whose stiffness is interpolated using Solid Isotropic Material with Penalization (SIMP). Gradients are computed with the adjoint method and the Method of Moving Asymptotes (MMA) is employed as the gradient-based optimizer. Two numerical examples related to a canonical pressure vessel and an optical mirror support structure are used to demonstrate the approach. Solutions are shown to satisfy minimum feature size requirements and designer-prescribed (process dependent) overhang constraint angles, while providing clear and crisp representations of topology. As observed in past works on overhang constraints, a clear trade-off is illustrated between the magnitude of the overhang constraint angle and the structural performance (mass or stiffness), with more strict requirements producing designs with lower performance.

Topology optimization for linear stationary stochastic dynamics: Applications to frame structures

In this work, an acoustic topology optimization method for structural surface design covered by porous materials is proposed. The analysis of acoustic problems is performed using the isogeometric boundary element method. Taking the element density of porous materials as the design variable, the volume of porous materials as the constraint, and the minimum sound pressure or maximum scattered sound power as the design goal, the topology optimization is carried out by solid isotropic material with penalization (SIMP) method. To get a limpid 0–1 distribution, a smoothing Heaviside-like function is proposed. To obtain the gradient value of the objective function, a sensitivity analysis method based on the adjoint variable method (AVM) is proposed. To find the optimal solution, the optimization problems are solved by the method of moving asymptotes (MMA) based on gradient information. Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems. Furthermore, the optimal distribution of sound-absorbing materials is highly frequency-dependent and usually needs to be performed within a frequency band.

Topology optimization for enhanced dynamic fracture resistance of structures

Topology optimization can devise structures with superior performance, while the results produced by topology optimization are often very complex and difficult to be manufactured directly. The additive manufacturing is a free-form manufacturing technique in which the component is built in a layer-by-layer manner. The integration of topology optimization and additive manufacturing technologies has the potential to bring significant synergy benefits. However, typical topology optimization algorithms have not considered the unique manufacturing limitations of additive manufacturing. This article focuses on the topology optimization for additive manufacturing considering self-supporting constraint based on the Solid Isotropic Material with Penalization (SIMP) framework. An explicit self-supporting constraint model is constructed, and the proposed method realizes self-supported by gradual evolution of supporting structures. The corresponding sensitivity analysis is investigated, which requires less computational cost and can be solved in parallel. Besides, a directional sensitivity filter is specifically proposed to promote the evolution of supporting structures. The performance and functionality of the proposed method is illustrated with three compliance minimization problems. All cases achieve self-supported successfully, and the solutions own good manufacturability.

A several cycles of design-verification-modification are needed during traditional design, which is very time-consuming. Topology optimization is rapidly expanding in the recent years in the field of structural mechanics. Currently it is widely applied to structural design. The combination of topology optimization and sizing and/or shape optimization has been adopted for flight vehicle structural design, which results possible better designs. In the paper, continuum structural topology optimizations as well as size optimization are combined for a folding wing structural design. A structure optimization problem is established using Solid Isotropic Material with Penalization (SIMP) method, it consists of the thickness variable of the skin and the relative element density variables of the tip part of the folding wing. The design objective is to minimize the compliance of the whole structure, and the constraints are structural mass constraints and stress constraints. The problem was solved based on commercial software package HyperWorks™. The resulting design shows that a new tip structure which satisfies the requirements of stiffness and strength was reconstructed.

Reliability-based topology optimization of fractionally-damped structures under nonstationary random excitation

Topological optimization is an innovative method to realize the lightweight design. This paper proposes a hybrid topology optimization method that combines the SIMP (solid isotropic material with penalization) method and genetic algorithm (GA), called the SIMP-GA method. In the method, SIMP is used to update the chromosomes, which can accelerate convergence. The filtering scheme in the SIMP method can filter unconnected elements to ensure the connectivity of the structure. We studied the influence of varying the filtering radius on the optimized structure. Simultaneously, in the SIMP-GA method, each element is regarded as a gene, which controls the population number to a certain extent, reduces the amount of calculation, and improves the calculation efficiency. The calculation of some typical examples proves that the SIMP-GA method can obtain a better solution than the gradient-based method. Compared with the conventional genetic algorithm and GA-BESO (Bi-directional Evolutionary Structural Optimization) method, the calculation efficiency of the proposed method is higher and similar results are obtained. The innovative topology optimization method could be an effective way for structural lightweight design.

Optimization of structures with complex shapes is a big challenge for computational physics. Results of numerical calculations show that composite or sandwich panel structures have a great influence on their effective properties. This article presents numerical results of optimization of sandwich panel properties. Calculations were provided for a three‐layer sandwich two‐phase composite. Optimization techniques were used for minimization of the effective Poisson's ratio of the core. The resultant composite structure exhibits a negative Poisson's ratio (NPR), although all its constituents are characterized by positive values of the Poisson's ratio. The structure of the composite is completely filled with solid materials, hence no voids appear within its whole volume. To find a solution, the finite‐element method combined with an optimization algorithm MMA (method of moving asymptotes) was used. For the purpose of analysis, the material parameters were written by means of the shape interpolation SIMP (solid isotropic material with penalization) scheme.

An integrated method of topological optimization and path design for 3D concrete printing

Topology optimization of Double-Double (DD) composite laminates considering stress control

In topology optimization of a continuum, it is important to consider stress-related objective or constraints, from both theoretical and application perspectives. It is known that the problem is challenging. Although remarkable achievements have been made with the SIMP (Solid Isotropic Material with Penalization) framework, a number of critical issues are yet to be fully resolved. In the paper, we present an approach of a shape equilibrium constraint strategy with the level-set/X-FEM framework. We formulate the topology optimization problem under (spatially-distributed) stress constraints into a shape equilibrium problem of active stress constraint. This formulation allows us to effectively handle the stress constraint, and the intrinsic non-differentiability introduced by local stress constraints is removed. The optimization problem is made into one of continuous shape-sensitivity and it is solved by evolving a coherent interface of the shape equilibrium concurrently with shape variation in the structural boundary during a level-set evolution process. Several numerical examples in two dimensions are provided as a benchmark test of the proposed shape equilibrium constraint strategy for minimum-weight and fully-stressed designs and for designs with stress constraint satisfaction.

Research on multi-stage topology optimization method based on latent diffusion model

Topology optimization has been successful in generating optimal topologies of various structures arising in real-world applications. Since these applications can have complex and large domains, topology optimization suffers from a high computational cost because of the use of unstructured meshes for discretization of these domains and their finite element analysis (FEA). This article addresses this challenge by developing three graphics processing unit (GPU)-based element-by-element strategies targeting unstructured all-hexahedral mesh for the matrix-free precondition conjugate gradient (PCG) finite element solver. These strategies mainly perform sparse matrix multiplication (SpMV) arising with the FEA solver by allocating more compute threads of GPU per element. Moreover, the strategies are developed to use shared memory of GPU for efficient memory transactions. The proposed strategies are tested with solid isotropic material with penalization (SIMP) method on four examples of 3D structural topology optimization. Results demonstrate that the proposed strategies achieve speedup up to 8.2 × over the standard GPU-based SpMV strategies from the literature.