Topology optimization for enhanced dynamic fracture resistance of structures

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.

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.

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.

The composite structures in the aerospace industry for in recent decades are widely applied however, at the beginning of the 21st century composites are growing rapidly. The largest companies in the aerospace industry are increasing the volume of composites application of in the structures, and nowadays the volume of composites reaches 50%. The different elements of aircraft and even highly loaded structures such as spars, ribs, skin, etc., are currently made from composites. First of all, this is due to the possibility of a significant reduction in the weight of the structure, as well as a decreasing in production costs. The advanced technologies in the engineering software allows to solute different complex problems. One of the main direct of research in the composites is optimization of composite structure due to improving the relative strength and relative stiffness of the composite structure, and improving the efficiency of manufacturing processes. There are a lot of methods of optimizations but currently the topological optimization is the most conceptual and forward-looking method. The main goal of the article is to analyze and estimate the approach for designing wing rib with symmetric laminated plates with the different fiber orientation based on the topology optimization. The following tasks were solved for this: firstly, a topological optimization model was determined. This model was based on maximum stiffness with a specified volume constraint is established. The next step was optimization by the solid isotropic material with penalization (SIMP) model and sensitivity filtering technique; as a result of optimization the topological structures of wing rib with different fibre orientations were obtained. The topological structure and stiffness of the wing rib depend on the fibre orientation. Finally, the corresponding morphing analysis of wing rib with laminated plates is implemented by adopting ANSYS, which verified the anti-deforming capability of topology structure and illustrated the feasibility for designing the wing rib. The result shows that the maximum deformation of optimized structure is 1.57mm, whereas the maximum deformation of the un-optimized structure is 2.02 mm. Under the condition of the same material removals, the optimized structure can decrease by more than 20% deformations.

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.

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.

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

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

Thermal design of composite cold plates by topology optimization

A topology optimization approach based on the boundary element method (BEM) and the optimality criteria (OC) method is proposed for the optimal design of sound absorbing material distribution within sound barrier structures. The acoustical effect of the absorbing material is simplified as the acoustical impedance boundary condition. Based on the solid isotropic material with penalization (SIMP) method, a topology optimization model is established by selecting the densities of absorbing material elements as design variables, volumes of absorbing material as constraints, and the minimization of sound pressure at reference surface as design objective. A smoothed Heaviside-like function is proposed to help the SIMP method to obtain a clear 0---1 distribution. The BEM is applied for acoustic analysis and the sensitivities with respect to design variables are obtained by the direct differentiation method. The Burton---Miller formulation is used to overcome the fictitious eigen-frequency problem for exterior boundary-value problems. A relaxed form of OC is used for solving the optimization problem to find the optimal absorbing material distribution. Numerical tests are provided to illustrate the application of the optimization procedure for 2D sound barriers. Results show that the optimal distribution of the sound absorbing material is strongly frequency dependent, and performing an optimization in a frequency band is generally needed.

A new multi-constraint optimization model with the weighted objective function is proposed to design the multi-input-multi-output (MIMO) compliant mechanisms. The main feature of this work is that both the two notable problems related to the de facto hinge and the movement coupling are tackled simultaneously in the topological synthesis of MIMO compliant mechanisms. To be specific, the first problem is the severe stress concentration in the flexible hinge areas, and it is solved by the introduction of input and output compliances into the objective function, which could facilitate the optimization to strike a good balance between structural flexibility and stiffness. The second problem is the high degree of control complexity caused by the coupled outputs and inputs, and it is addressed by achieving the complete decoupling with two groups of extra constraints that are used to suppress the input coupling and the output coupling, respectively. As the most common and effective topology optimization method, the Solid Isotropic Material with Penalization (SIMP)-based density method is adopted here to obtain the optimized configurations. After the analytical sensitivity deduction related to the weighted objective function and constraints, two typical numerical examples are presented to demonstrate the validity of the proposed topology optimization framework in designing the hinge-free and completely decoupled MIMO compliant mechanisms.

This paper discusses a geometrical optimization method for thermoelectric generators. Our method provides the optimized geometry in accord with various arbitrary conditions such as types of materials, volume of materials, temperatures of installation position, and shape of installation position. It has the potential to contribute to improving thermoelectric devices in supporting design stages. By establishing the coupled equations of state for the thermoelectric problem, an analytical model subject to these equations is introduced that mimics the closed circuit composed of the thermoelectric materials, electrodes and a resistor. The total electric power lost through the resistor is formulated as an objective function for optimization. The proposed optimization method for thermoelectric generators is implemented as a geometrical optimization method using the solid isotropic material with penalization (SIMP) method used in topology optimizations. Simple relations are formulated between the density function of SIMP method and physical properties of thermoelectric material. Sensitivity analysis for the objective function is formulated with respect to the density function and the adjoint equations required for calculating it. Depending on the sensitivity, the density function is updated using the method of moving asymptotes, which has numerous benefits in various optimization problems by virtue of its combination with topology optimization. Finally, the numerical examples are provided to demonstrate the validity of our method.

Electro-thermal-compliant mechanisms are mechanisms onto which electric voltage is applied as input. This mechanism is based on the thermal expansion properties of the materials. This study considered all of the convection effects according to layouts produced after each topology optimization process. A new material mixing method based on bi-directional evolutionary structural optimization (BESO) was suggested to obtain optimal topologies for compliant mechanisms composed of two materials. Reliability-based topology optimization (RBTO) based on BESO was also applied to the topology optimizations of the mechanisms. Performance measurement approach (PMA), which estimates has probabilistic constraints that are formulated in terms of the reliability index, was adopted to evaluate the probabilistic constraints. The procedure has been tested in numerical applications, and the results were compared with those obtained by the level set and solid isotropic material with penalization (SIMP) methods for validation of the proposed approaches.

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.