Optimal placement of active material actuators using genetic algorithm

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.

SummaryOn account of the inevitable multisource uncertainty factors in compliant mechanisms, which seriously affect the accuracy of output motion, a nonprobabilistic reliability–based topology optimization (NRBTO) framework for compliant mechanisms with interval uncertainties is introduced. Combined with the solid isotropic material with penalization (SIMP) model and the set‐theoretical interval method, the uncertainty quantification analysis is conducted to obtain mathematical approximations and boundary laws of considered mean compliance. By normalization treatment of the limit‐state function, a new quantified measure of the nonprobabilistic reliability is then defined. The compliance‐based NRBTO design method ensures the output motion realizing its target value accurately considering the uncertainty factors. The sensitivities of the nonprobabilistic reliability index with respect to design variables are calculated by the adjoint vector method. Two engineering examples are eventually presented to illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques.

The SIMP (solid isotropic material with penalization) approach is perhaps the most popular density variable relaxation method in topology optimization. This method has been very successful in many applications, but the optimization solution convergence can be improved when new variables, not the direct density variables, are used as the design variables. In this work, we newly propose S-shape functions mapping the original density variables nonlinearly to new design variables. The main role of S-shape function is to push intermediate densities to either lower or upper bounds. In particular, this method works well with nonlinear mathematical programming methods. A method of feasible directions is chosen as a nonlinear mathematical programming method in order to show the effects of the S-shape scaling function on the solution convergence.

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.

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.

This paper develops a non-probabilistic reliability-based topology optimization (NRBTO) framework for continuum structures under multi-dimensional convex uncertainties. Combined with the solid isotropic material with penalization (SIMP) model and the set-theoretical convex method, the uncertainty quantification (UQ) analysis is firstly conducted to obtain mathematical approximations and boundary laws of considered displacement responses. By normalization treatment of the limit-state function, a new quantified measure of the non-probabilistic reliability is then defined and further deduced by the principle of the hyper-volume ratio. For circumventing optimization difficulties arising from large-scale design variables, the adjoint vector scheme for sensitivity analysis of the reliability index with respect to design variables are discussed as well. Numerical applications eventually illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques.

Conventional topology optimization is concerned with the structures modeled by classical theory of mechanics. Since it does not consider the effects of the microstructures of materials, the classical theory can not reveal the size effect due to material’s heterogeneity. Couple-stress theory, which takes account of the microscopic properties of the material, is capable of describing the size effect in deformations. The purpose of this paper is to investigate the formulation for topology optimization of couple-stress material structures. The artificial material density of each element is chosen as design variable. Based on the basic idea of SIMP (Solid Isotropic Material with Penalization) method, the effective material stiffness matrix of couple-stress material is related to the artificial density by power law with penalty. The structural analysis is implemented by finite element method for couple-stress materials, and a 4-noded quadrilateral couple-stress element is formulated in which C1 continuity requirement is relaxed. Some typical problems are solved and the optimal results based on the couple-stress theory are compared with the conventional ones. It is found that the optimal topologies of couple-stress continuum show remarkable size effect.

An isogeometric approach of two dimensional acoustic design sensitivity analysis and topology optimization analysis for absorbing material distribution

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

This article investigates the study of Topology Optimization (TO) in 3D elasticity problems to determine the optimal topology by applying the evolutionary methods of Smoothing Evolutionary Structural Optimization (SESO), Sequential Element Rejection and Admission (SERA), and Evolutionary Structural Optimization (ESO). These procedures were implemented in MATLAB code as an extension of Top3d implemented for SIMP by using the eight-node hexahedral finite element formulation in three-dimensional elastostatic structures. The approaches conducted in the present study are demonstrated with numerical examples involving the compliance minimization criterion. Further, a brief synthesis of flexible mechanisms was studied to emphasize the performance of complaint mechanisms measured in terms of two design specifications/functionalities: mechanical and geometrical advantages, which are the highlights of this article. To show the gains of the proposed methods, numerical results obtained are compared with Solid Isotropic Material with Penalization (SIMP) models.

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.

Move limits definition in structural optimization with sequential linear programming. Part II: Numerical examples

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.

This article develops a multi-resolution topology optimization (MTOP) approach based on the solid isotropic material with penalization (SIMP) method, which is effective in obtaining high-resolution designs at low computational cost. The extended finite element method (XFEM) is employed to decouple the analysis mesh, material description and nodal design variables. By the advantage of XFEM at modelling material discontinuity, detailed geometrical features are generated on a coarse analysis mesh. To obtain a clear interface between material grids, a variation of the traditional sensitivity filter is introduced to produce discrete solutions. The low computational costs make the proposed approach appropriate for dealing with problems requiring a high number of finite element analysis (FEA) processes, typically high-resolution/large-scale models, stress minimization, etc. Accurate von Mises stress is calculated on a high number of Gaussian points, making the approach perform better at stress minimization. Then, several 2D and 3D examples optimized by different solvers are illustrated to demonstrate the effectiveness and excellent generality of the proposed approach.

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