A strain based topology optimization method for compliant mechanism design

The Energy based topology optimization method has been used in the design of compliant mechanisms for many years. Although many successful examples from the energy based topology optimization method have been presented, optimized configurations of these designs are often very similar to their rigid linkage counterparts; except using compliant joints in place of rigid links. These complaint joints will endure large strain under the applied forces in order to perform the specified motions which are very undesirable in a compliant mechanism design. In this paper, a strain based topology optimization method is proposed to avoid a localized high strain of the compliant mechanism design, which is one of the drawbacks using strain energy formulation. Therefore, instead of minimizing the strain energy for structural rigidity, a global effective strain function is minimized. This is done in order to distribute the strain within the entire mechanism while maximizing the structural rigidity. Furthermore, the physical programming method is adopted to accommodate both flexibility and rigidity design objectives. Design examples from both the strain energy based topology optimization and the strain based method are presented and discussed.     

Finite prism method based topology optimization of beam cross section for buckling load maximization

The use of the finite element method (FEM) for buckling topology optimization of a beam cross section requires large numerical cost due to the discretization in the length direction of the beam. This investigation employs the finite prism method (FPM) as a tool for linear buckling analysis, reducing degrees of freedom of three-dimensional nodes of FEM to those of two-dimensional nodes with the help of harmonic basis functions in the length direction. The optimization problem is defined as the maximization problem of the lowest eigenvalue, for which a bound variable is introduced and set as the design objective to treat mode switching phenomena of multiple eigenvalues. The use of the bound formulation also helps the proposed optimization to treat beams having local plate buckling modes as the fundamental modes as well as beams having global buckling modes. The axial stress is calculated according to the distribution of material modulus which is interpolated using the SIMP approach. Optimization problems finding cross-section layouts from rectangular, L-shaped and generally-shaped design domains are solved for various beam lengths to ascertain the effectiveness of the proposed method.     

Eigenfrequency constrained topology optimization of finite strain hyperelastic structures

Structural and Multidisciplinary Optimization - This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology...     

基于层连优化的新型小世界神经网络

对多层前向小世界神经网络的网络参数、权值修正策略以及网络结构进行改进, 提出一种基于层连优化的小世界神经网络的改进算法. 通过对比现有各种不同形式的小世界神经网络, 验证了上述改进的必要性. 仿真结果表明, 改进模型比现有小世界神经网络收敛速度更快, 逼近精度更高, 模型稳定性更强.     

Stress and strain control via level set topology optimization

This paper presents a level set topology optimization method for manipulation of stress and strain integral functions in a prescribed region (herein called sub-structure) of a linear elastic domain. The method is able to deviate or concentrate the flux of stress in the sub-structure by optimizing the shape and topologies of the boundaries outside of that region. A general integral objective function is proposed and its shape sensitivities are derived. For stress isolation or maximization, a von Mises stress integral is used and results show that stresses in the sub-structure can be drastically reduced. For strain control, a strain integral combined with a vector able to select the component of the strain is used. A combination of both can be used to minimize deformation of a prescribed direction. Numerical results show that strain can be efficiently minimized or maximized for a wide range of directions. The proposed methodology can be applied to stress isolation of highly sensitive non strain-based sensors, design for failure, maximization of mechanical strain and strain direction control for strain-based sensors and microdevices.     

Miniaturization of patch antenna based on hybrid topology optimization

A hybrid topology optimization method that combines the scalar isotropic material with penalization and the level set method is utilized to achieve the miniaturization of patch antennas while maintaining good radiation and polarization characteristics. In order to achieve this goal, the Heaviside projection filter is applied to obtain topologies that are more complex. Both the radiation power and the reflection coefficient of the antenna are utilized as sub‐objectives. Besides, by setting the radiation patch to be symmetrical, not only the numbers of optimization variables and optimization sub‐objectives are reduced, but also the cross‐polarization level is suppressed effectively, so that the optimization is accelerated. The optimized patch antenna achieves good performance in patch size, impedance matching, radiation pattern, gain, and polarization characteristics. Compared with the reference patch antenna, the patch size of the optimized antenna is reduced by 63%, while the maximum realized gain and efficiency remain basically unchanged, achieving more than 5.9 dBi and 90%, respectively. Due to its very small size patch, the antenna is particularly suitable for compact multi‐antenna and antenna array applications.     

Topology optimization based on finite strain plasticity

In this paper infinitesimal elasto-plastic based topology optimization is extended to finite strains. The employed model is based on rate-independent isotropic hardening plasticity and to separate the elastic deformation from the plastic deformation, use is made of the multiplicative split of the deformation gradient. The mechanical balance laws are solved using an implicit total Lagrangian formulation. The optimization problem is solved using the method of moving asymptotes and the sensitivity required to form convex separable approximations is derived using a path-dependent adjoint strategy. The optimization problem is regularized using a PDE-type filter. A simple boundary value problem where the plastic work is maximized is used to demonstrate the capability of the presented model. The numerical examples reveal that finite strain plasticity successfully can be combined with topology optimization.     

Elephant herding optimization using dynamic topology and biogeography-based optimization based on learning for numerical optimization

With the increasing complexity of optimization problems in the real world, more and more intelligent algorithms are used to solve these problems. Elephant herding optimization (EHO), a recently proposed metaheuristic algorithm, is based on the nomadic habits of elephants on the grassland. The herd is divided into multiple clans, each individual drawing closer to the patriarchs (clan updating operator), and the adult males are separated during puberty (separating operator). Biogeography-based optimization (BBO) is inspired by the principles of biogeography, and finally achieves an equilibrium state by species migration and drifting between geographical regions. To solve the numerical optimization problems, this paper proposes an improved elephant herding optimization using dynamic topology and biogeography-based optimization based on learning, named biogeography-based learning elephant herding optimization (BLEHO). In BLEHO, we change the topological structure of the population by dynamically changing the number of clans of the elephants. For the updating of each individual, we use the update of the operator based on biogeography-based learning or the operator based on EHO. In the separating phase, we set the separation probability according to the number of clans, and adopt a new separation operator to carry out the separation operation. Finally, through elitism strategy, a certain number of individuals are preserved directly to the next generation without being processed, thus ensuring a better evolutionary process for the population. To verify the performance of BLEHO, we used the benchmarks provided by IEEE CEC 2014 for the test. The experimental results were compared with some classical algorithms (ABC, ACO, BBO, DE, EHO, GA, and PSO) and the most advanced algorithms (BBKH, BHCS, CCS, HHO, PPSO, SCA, and VNBA) and analyzed by Friedman rank test. Finally, we also applied BLEHO to the simple traveling salesman problem (TSP). The results show that BLEHO has better performance than other methods.

     

Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties

This paper discusses a new structural optimization method, based on topology optimization techniques, using frame elements where the cross-sectional properties can be treated as design variables. For each of the frame elements, the rotational angle denoting the principal direction of the second moment of inertia is included as a design variable, and a procedure to obtain the optimal angle is derived from Karush–Kuhn–Tucker (KKT) conditions and a complementary strain energy-based approach. Based on the above, the optimal rotational angle of each frame element is obtained as a function of the balance of the internal moments. The above methodologies are applied to problems of minimizing the mean compliance and maximizing the eigen frequencies. Several examples are provided to show the utility of the presented methodology.     

Multiform frequency selective surfaces optimal design based on topology optimization

This article proposes an optimization design method for various frequency selective surfaces (FSSs) based on topology optimization algorithm incorporated with the genetic algorithm. The present method takes the connectivity condition both in simulation and fabrication of the elements into consideration. For the filling elements structural design methodology, the novel hexagonal‐pixel filling element structural design is employed for improving the patch connection. As examples, various FSSs, such as a large‐angle‐stability band‐pass FSS, wideband band‐pass FSS, and multiple band‐pass FSS, are designed. Furthermore, the validity of the present method is proved by the agreement between the simulation and the measurement.     

基于冯诺依曼拓扑结构的骨干粒子群优化算法

为了改善骨干粒子群优化BBPSO算法的易早熟、易陷入局部最优解等缺点,提出了一种基于冯诺依曼拓扑结构的改进骨干粒子群优化VBBPSO算法。新算法提出"兼顾落后粒子"概念,通过应用冯诺依曼拓扑结构构造邻域,用邻域最优解取代全局最优解,引入中心项调节系数,在邻域范围内调整BBPSO算法的进化中心项与离散控制项,提高了算法全局探索能力与局部开发能力。实验结果表明,较几种经典的BBPSO算法,VBBPSO算法的综合性能有明显提升。     

Support structure design in additive manufacturing based on topology optimization

A support structure design technique for additive manufacturing (AM) is proposed that minimizes the deformation while using the least amount of support material, minimizes the time required to add the supports, and designs supports that are easily removed. This study presents a repulsion index (RI), which satisfies the easy removal requirement and minimizes the number of artifacts left on the specimen surface, and a weighting function, which quantifies the cost incurred by the time taken to build the supports. A multi-objective topological optimization based on the simple isotropic material with penalization method, continuous approximation of material distribution, and method of moving asymptotes is formulated that includes the proposed RI and cost formulation. Numerical simulations demonstrate that rational support layouts can be determined with the proposed cost-based formulation in the topological optimization, allowing designers to find design solutions with a compromise between specimen surface profile error and support structure costs.     

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。     

基于星间网络拓扑技术的星间链路优化设计

摘要：在星间网络环境中,全链路生命周期达不到预期标准数值,进而导致拓扑信道传输特性不能得到满足,基于此现状,设计星间网络拓扑技术支持下的星间链路优化方法。在网络拓扑框架中,规划星间传感器节点的具体位置,推导拓扑演化所需的机制条件,提升全链路组织中数据信息的理想生命周期数值,完成星间网络的拓扑结构设计。在此基础上,研究星间链路的基本结构形式,判断处理优化流程的合理性,根据具体的优化设计建立条件,完成静态与动态链路的优化设计,实现星间链路优化设计的条件与流程完善。联合LDPC码,构造标准的星间校验矩阵,并处理信道中编码数据的译码形态,满足拓扑信道的传输特性,完成星间信道的LDPC编码,实现基于星间网络拓扑技术的星间链路优化设计。建立星间网络环境进行比对性实验,数据结果显示优化后星间链路生命周期最大值提升至135ms,WIT指标数值始终保持在70%左右,拓扑信道传输特性得到满足。     

Truncated hierarchical B-spline–based topology optimization

Structural and Multidisciplinary Optimization - This work presents a truncated hierarchical B-spline–based topology optimization (THB-TO) to address topology optimization (TO) for both...     

Shape and topology optimization based on the convected level set method

The aim of this research is to construct a shape optimization method based on the convected level set method, in which the level set function is defined as a truncated smooth function obtained by using a sinus filter based on a hyperbolic tangent function. The local property of the hyperbolic tangent function dramatically reduces the generation of red the error between the specified profile of the hyperbolic tangent function and the level set function that is updated using a time evolution equation. In addition, the small size of the error facilitates the use of convective reinitialization, whose basic idea is that the reinitialization is embedded in the time evolution equation, whereas such treatment is typically conducted in a separate calculation in conventional level set methods. The convected level set method can completely avoid the need for additional calculations when performing reinitialization. The validity and effectiveness of our presented method are tested with a mean compliance minimization problem and a problem for the design of a compliant mechanism.     

Structural topology optimization based on non-local Shepard interpolation of density field

This paper presents a non-local density interpolation strategy for topology optimization based on nodal design variables. In this method, design variable points can be positioned at any locations in the design domain and may not necessarily coincide with elemental nodes. By using the Shepard family of interpolants, the density value of any given computational point is interpolated by design variable values within a certain circular influence domain of the point. The employed interpolation scheme has an explicit form and satisfies non-negative and range-restricted properties required by a physically significant density interpolation. Since the discretizations of the density field and the displacement field are implemented on two independent sets of points, the method is well suited for a topology optimization problem with a design domain containing higher-order elements or non-quadrilateral elements. Moreover, it has the ability to yield mesh-independent solutions if the radius of the influence domain is reasonably specified. Numerical examples demonstrate the validity of the proposed formulation and numerical techniques. It is also confirmed that the method can successfully avoid checkerboard patterns as well as “islanding” phenomenon.     

基于拓扑结构与粒子变异改进的粒子群优化算法

为使粒子群优化算法(PSO)优化过程的多样性与收敛性得到合理解决,以提高算法优化性能,基于种群拓扑结构与粒子变异提出两种粒子群改进算法RSMPSO和RVMPSO.改进算法将具有信息定向流动的闭环拓扑结构与星型拓扑结构或四边形拓扑结构相结合,促使粒子在前期寻优过程中具有较高的多样性,保证搜索的广度,而在后期满足粒子群的整体收敛性,保证寻优的精度.同时,将布谷鸟搜索算法(CS)中的偏好随机游走变异策略引入改进算法中,增强粒子跳出局部最优的能力.对标准测试函数的仿真实验表明,所改进的PSO算法与其他6个对比算法相比不仅操作简单,优化精度高,而且在算法收敛性及稳健性方面都有着更出色的表现.     

Stress-constrained continuum topology optimization: a new approach based on elasto-plasticity

A new approach for generating stress-constrained topological designs in continua is presented. The main novelty is in the use of elasto-plastic modeling and in optimizing the design such that it will exhibit a linear-elastic response. This is achieved by imposing a single global constraint on the total sum of equivalent plastic strains, providing accurate control over all local stress violations. The single constraint essentially replaces a large number of local stress constraints or an approximate aggregation of them – two common approaches in the literature. A classical rate-independent plasticity model is utilized, for which analytical adjoint sensitivity analysis is derived and verified. Several examples demonstrate the capability of the computational procedure to generate designs that challenge results from the literature, in terms of the obtained stiffness-strength-weight trade-offs. A full elasto-plastic analysis of the optimized designs shows that prior to the initial yielding, these designs can sustain significantly higher loads than minimum compliance topological layouts, with only a minor compromise on stiffness.