On equal-width length-scale control in topology optimization

This paper deals with equal-width length-scale control in topology optimization. To realize this aim, we first review different notions of minimum and maximum length-scale control and highlight some perhaps counterintuitive consequences of the various definitions. Here, we implement equal-width control within the moving morphable components (MMC) framework by imposing the same upper and lower bounds on the width of the components. To avoid partially overlapping beams and nearly parallel beams, as well as beams crossing at small angles, we introduce penalty functions of the angle difference and the minimum distance between any two beams. A penalized optimization formulation of compliance minimization is established and studied in several numerical examples with different load cases and boundary conditions. The numerical results show that equal-width length-scale control can be obtained by using the proposed penalty function in combination with a continuation approach for the amount of penalization.

     

基于网络拓扑优化的WSN最小跳路由算法

以节能为主要目标,基于最小跳路由的思想提出一种基于网络拓扑优化的WSN最小跳路由算法——MH-TO算法。该算法采用折半匹配的功率调整策略对网络拓扑进行优化,并引入“塔模型”实现节点的最小跳信息的学习,使得信息包路由时沿着最小跳的路径向sink节点传送。理论分析和仿真实验结果表明,与基于最小跳数场的自组织路由算法相比,该算法能够降低能量消耗并均衡能量负载,从而显著延长网络的生存期。     

GPU parallel strategy for parameterized LSM-based topology optimization using isogeometric analysis

This paper proposes a new level set-based topology optimization (TO) method using a parallel strategy of Graphics Processing Units (GPUs) and the isogeometric analysis (IGA). The strategy consists of parallel implementations for initial design domain, IGA, sensitivity analysis and design variable update, and the key issues in the parallel implementation, e.g., the parallel assembly race condition, are discussed in detail. The computational complexity and parallelization of the different steps in the TO are also analyzed in this paper. To better demonstrate the advantages of the proposed strategy, we compare efficiency of serial CPU, multi-thread parallel CPU and GPU by benchmark examples, and the speedups achieve two orders of magnitude.     

Revisiting topology optimization with buckling constraints

Structural and Multidisciplinary Optimization - We review some features of topology optimization with a lower bound on the critical load factor, as computed by linearized buckling analysis. The...     

Multi-material topology optimization with strength constraints

A heuristic approach to handle strength constraints based on material failure criteria in multi-material topology optimization is presented. This is particularly advantageous if different materials have different failure criteria. The change in the material failure function in an element due to a contemplated material change is estimated without the need for expensive matrix factorizations. This change is used along with the changes to the objective and deflection-based constraint functions, computed using pseudo-sensitivities, to determine a single aggregated ranking parameter for the element. Elements are ranked on the basis of their ranking parameters and this rank is used to modify the material ID-s of a few top-ranked elements during an optimization iteration. The working of the algorithm is demonstrated on a few example problems showing its effectiveness and utility in deriving optimal topologies with multiple materials in the presence of stress and strain-based failure criteria, in addition to the conventional stiffness-based constraints.     

Misalignment topology optimization with manufacturing constraints

Structural and Multidisciplinary Optimization - This work aims at introducing misalignment response in the design of mechanical transmission components using topology optimization. Misalignment...     

Optimality criteria method for topology optimization under multiple constraints

The existing framework of optimality criteria method is limited to the optimization of a simple energy functional with a single constraint on material resource. The present work extends the optimality criteria method to the case of multiple constraints. The difficulty in updating the Lagrangian multipliers is treated by gradient-split Taylor series expansion. Applications of the method are illustrated by computing the optimal structures under multiple displacement constraints, and by designing the material cells under given macroscopic elastic tensors that correspond to both positive and negative Poisson's ratios.     

Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model

Using a quantified measure for non-probab ilistic reliability based on the multi-ellipsoid convex model, the topology optimization of continuum structures in presence of uncertain-but-bounded parameters is investigated. The problem is formulated as a double-loop optimization one. The inner loop handles evaluation of the non-probabilistic reliability index, and the outer loop treats the optimum material distribution using the results from the inner loop for checking feasibility of the reliability constraints. For circumventing the numerical difficulties arising from its nested nature, the topology optimization problem with reliability constraints is reformulated into an equivalent one with constraints on the concerned performance. In this context, the adjoint variable schemes for sensitivity analysis with respect to uncertain variables as well as design variables are discussed. The structural optimization problem is then solved by a gradient-based algorithm using the obtained sensitivity. In the present formulation, the uncertain-but bounded uncertain variations of material properties, geometrical dimensions and loading conditions can be realistically accounted for. Numerical investigations illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques. The computational results also reveal that non-probabilistic reliability-based topology optimization may yield more reasonable material layouts than conventional deterministic approaches. The proposed method can be regarded as an attractive supplement to the stochastic reliability-based topology optimization.     

Eigenvalue topology optimization of structures using a parameterized level set method

Preventing a structure from resonance is important in many real-world applications. Because an external excitation frequency can be lower than the fundamental eigenfrequency or between the eigenfrequencies of a structure, there is a strong need for eigenfrequency optimization technology to optimize the fundamental eigenfrequency and, in addition, the k-th eigenfrequency and to maximize the gap between eigenfrequencies. However, previous optimization studies on vibrating elastic structures that used the level set method have been devoted to the optimization of the fundamental eigenfrequency, whereas the higher-order eigenfrequencies optimization problem has seldom been considered. This paper presents an eigenfrequency optimization technology that is based on the compactly supported radial basis functions (CS-RBFs) parameterized level-set method, using the fundamental eigenfrequency, the eigenfrequency of a given higher-order, and the gap between two consecutive eigenfrequencies as the optimization objectives. Furthermore, to address the oscillation problem of the objective function, we adopt an exponential weighted optimization model of a number of the lower eigenfrequencies for multiple eigenvalue optimizations, and we utilize mode-tracking technology for the single eigenvalue optimization.In addition, we further extend the CS-RBFs parameterized level-set method to an optimization that is performed with geometric constraints, which means that the size and position of the regular holes in the structure can be optimized with the shape and topology. This approach is useful in real-world applications. The effectiveness of this method is demonstrated by several widely investigated examples that have various objectives.     

Semantic constraints for membership function optimization

The optimization of fuzzy systems using bio-inspired strategies, such as neural network learning rules or evolutionary optimization techniques, is becoming more and more popular. In general, fuzzy systems optimized in such a way cannot provide a linguistic interpretation, preventing us from using one of their most interesting and useful features. This paper addresses this difficulty and points out a set of constraints that when used within an optimization scheme obviate the subjective task of interpreting membership functions. To achieve this a comprehensive set of semantic properties that membership functions should have is postulated and discussed. These properties are translated in terms of nonlinear constraints that are coded within a given optimization scheme, such as backpropagation. Implementation issues and one example illustrating the importance of the proposed constraints are included     

Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures

This paper presents a novel concurrent topology optimization approach for finding the optimum topologies of macrostructures and their corresponding parameterized lattice microstructures in an integrated manner. Considering the manufacturability of the structure designs and computational efficiency, additional parameters are introduced to define the microstructure unit cell patterns and their non-uniform distribution, which avoids expensive iterative numerical homogenization calculations during topology optimization and results in an easier modelling of structure designs as well. It is worth mentioning that the equivalent properties of material microstructures serve as a link between the macro and the micro scale with the help of homogenization theory and the Porous Anisotropic Material with Penalization (PAMP) model. Besides, sensitivities of global structure compliance with respect to the pseudo-density variables and the microstructure parameter variables are derived, respectively. Moreover, several numerical examples are presented and reasonable solutions have been obtained to demonstrate the efficiency of the proposed method. Finally, mechanical testing is conducted to investigate the better performance of the optimized structure which is fabricated by 3D printing.     

Stress constraints sensitivity analysis in structural topology optimization

Sensitivity Analysis is an essential issue in the structural optimization field. The calculation of the derivatives of the most relevant quantities (displacements, stresses, strains) in optimum design of structures allows to estimate the structural response when changes in the design variables are introduced. This essential information is used by the most frequent conventional optimization algorithms (SLP, MMA, Feasible directions) in order to reach the optimal solution. According to this idea, the Sensitivity Analysis of the stress constraints in Topology Optimization problems is a crucial aspect to obtain the optimal solution when stress constraints are considered.Maximum stiffness approaches usually involve one linear constraint and one non-linear objective function. Thus, the computation of the required sensitivity analysis does not mean a crucial limitation. However, in the topology optimization problem with stress constraints, efficient and accurate computation of the derivatives is needed in order to reach appropriate optimal solutions. In this paper, a complete analytic and efficient procedure to obtain the Sensitivity Analysis of the stress constraints in topology optimization of continuum structures is analyzed. First order derivatives and second order directional derivatives of the stress constraints are analyzed and included in the optimization procedure. In addition, topology optimization problems usually involve thousands of design variables and constraints. Thus, an efficient implementation of the algorithms used in the computation of the Sensitivity Analysis is developed in order to reduce the computational cost required. Finally, the sensitivity analysis techniques presented in this paper are tested by solving some application examples.     

Non-probabilistic robust continuum topology optimization with stress constraints

Structural and Multidisciplinary Optimization - This paper proposes a non-probabilistic robust design approach, based on optimization with anti-optimization, to handle unknown-but-bounded loading...     

The parameterized level set method for structural topology optimization with shape sensitivity constraint factor

In recent years, the parameterized level set method (PLSM) has attracted widespread attention for its good stability, high efficiency and the smooth result of topology optimization compared with the conventional level set method. In the PLSM, the radial basis functions (RBFs) are often used to perform interpolation fitting for the conventional level set equation, thereby transforming the iteratively updating partial differential equation (PDE) into ordinary differential equations (ODEs). Hence, the RBFs play a key role in improving efficiency, accuracy and stability of the numerical computation in the PLSM for structural topology optimization, which can describe the structural topology and its change in the optimization process. In particular, the compactly supported radial basis function (CS-RBF) has been widely used in the PLSM for structural topology optimization because it enjoys considerable advantages. In this work, based on the CS-RBF, we propose a PLSM for structural topology optimization by adding the shape sensitivity constraint factor to control the step length in the iterations while updating the design variables with the method of moving asymptote (MMA). With the shape sensitivity constraint factor, the updating step length is changeable and controllable in the iterative process of MMA algorithm so as to increase the optimization speed. Therefore, the efficiency and stability of structural topology optimization can be improved by this method. The feasibility and effectiveness of this method are demonstrated by several typical numerical examples involving topology optimization of single-material and multi-material structures.

     

Canonical constraints for parameterized data types

This paper presents a comparatively general method for specifying a ‘data constraint’ on a parameterized data type (i.e., specifying just which category of algebras it is supposed to be defined or correct on), and shows that there is a simple canonical form for such constraint specifications. We also show how such constraints may be employed to give ‘loose’ specifications of data types.     

A Multi-point constraints based integrated layout and topology optimization design of multi-component systems

Structural and Multidisciplinary Optimization - The integrated layout and topology optimization is to find proper layout of movable components and topology patterns of their supporting structures,...     

Heaviside projection based topology optimization by a PDE-filtered scalar function

This paper deals with topology optimization based on the Heaviside projection method using a scalar function as design variables. The scalar function is then regularized by a PDE based filter. Several image-processing based filtering techniques have so far been proposed for regularization or restricting the minimum length scale. They are conventionally applied to the design sensitivities rather than the design variables themselves. However, it causes discrepancies between the filtered sensitivities and the actual sensitivities that may confuse the optimization process and disturb the convergence. In this paper, we propose a Heaviside projection based topology optimization method with a scalar function that is filtered by a Helmholtz type partial differential equation. Therefore, the optimality can be strictly discussed in terms of the KKT condition. In order to demonstrate the effectiveness of the proposed method, a minimum compliance problem is solved.     

An explicit parameterization for casting constraints in gradient driven topology optimization

From a practical point of view it is often desirable to limit the complexity of a topology optimization design such that casting/milling type manufacturing techniques can be applied. In the context of gradient driven topology optimization this work studies how castable designs can be obtained by use of a Heaviside design parameterization in a specified casting direction. This reduces the number of design variables considerably and the approach is simple to implement.