Articulated mechanism design with a degree of freedom constraint

This paper deals with design of articulated mechanism using a truss‐based ground‐structure representation. The proposed method can accommodate extremely large displacement by considering geometric non‐linearity. In addition, it can also control the mechanical degrees of freedom (DOF) of the resultant mechanism by using a DOF equation based on Maxwell's rule. The optimization is based on a relaxed formulation of an original integer problem and also involves developments directed at handling the redundancy inherent in the ground‐structure representation. One planar test example is selected as the basis for the developments so as to compare the proposed method with other alternative approaches including a graph‐theoretical enumeration approach which guarantees the identification of the globally optimal solution. Also, an inverter problem is treated where a continuation method is required in order to direct the optimization algorithm towards an integer solution. Copyright © 2004 John Wiley & Sons, Ltd.     

A robust dual algorithm for topology design of structures in discrete variables

Dual optimization algorithms for the topology optimization of continuum structures in discrete variables are gaining popularity in recent times since, in topology design problems, the number of constraints is small in comparison to the number of design variables. Good topologies can be obtained for the minimum compliance design problem when the perimeter constraint is imposed in addition to the volume constraint. However, when the perimeter constraint is relaxed, the dual algorithm tends to give bad results, even with the use of higher‐order finite element models as we demonstrate in this work. Since, a priori, one does not know what a good value of the perimeter to be specified is, it is essential to have an algorithm which generates good topologies even in the absence of the perimeter constraint. We show how the dual algorithm can be made more robust so that it yields good designs consistently in the absence of the perimeter constraint. In particular, we show that the problem of checkerboarding which is frequently observed with the use of lower‐order finite elements is eliminated. Copyright © 2001 John Wiley & Sons, Ltd.     

3-RPRR类平面全柔性并联机构拓扑优化设计

针对全柔性并联机构的构型设计不能满足精密定位和微纳制造领域的需求,为提高全柔性并联机构的整体刚度、抗振性和抗干扰性,基于3-RPRR并联机构原型,采用型综合法,设计出与并联机构原型空间运动特性一致的3-RPRR类平面全柔性机构及其支链.运用拓扑优化的方法,得到铰链最优配置的3-RPRR类平面全柔性并联机构及其支链.采用Hyperworks/Radioss软件分别对这2种3-RPRR类平面全柔性并联机构进行静力学及模态分析,仿真结果表明:在实现相同运动特性的前提下,优化后的3-RPRR类平面全柔性并联机构不仅节省材料,而且在刚度、抗振性和抗干扰性方面更优.     

A novel reliability-based topology optimization framework for the concurrent design of solid and truss-like material structures with unknown-but-bounded uncertainties

A new nonprobabilistic reliability-based topology optimization method for continuum structures with displacement constraints is proposed in this paper, in which the optimal layout consists of solid material and truss-like microstructure material simultaneously. The unknown-but-bounded uncertainties that exist in material properties, external loads, and safety displacements are considered. By utilizing the representative volume element analysis, rules of macro-micro stiffness performance equivalence can be confirmed. A solid material and truss-like microstructure material structure integrated design interpolation model is firstly constructed, in which design domain elements can be conducted to select solid material or truss-like microstructure material by a combination of the finite element method in the topology optimization process. Moreover, a new nonprobabilistic reliability measuring index, namely, the optimization feature distance is defined by making use of the area-ratio ideas. Furthermore, the adjoint vector method is employed to obtain the sensitivity information between the reliability measure and design variables. By utilizing the method of moving asymptotes, the investigated optimization problem can be iteratively solved. The effectiveness of the developed methodology is eventually demonstrated by two examples.     

Simultaneous optimal design of topology and size for a flexure-hinge-based guiding mechanism to minimize mass under stiffness and frequency constraints

The guiding mechanism based on flexure hinges (FHs) is widely used in micro/nano-manufacturing technology. Both the stiffness and the frequency of FHs play significant roles in their dynamic performance, so the design task of such a structure is to find the optimal topology and corresponding size of FHs under stiffness and frequency constraints. However, the existing optimization methods pay more attention to the stiffness than to the frequency constraint owing to difficulties in dynamic topology optimization. In this article, with the symmetrical layout assumption of FHs and the analytical equivalent stiffness and mass expression of a single FH, the simultaneous topology and size optimization problem is converted to an analytical optimization formula with both discrete and continuous variables. Finally, the tension stiffening effect is used to compensate for manufacturing errors. A design case is used to illustrate the efficiency of the proposed method.     

A bidirectional evolutionary structural optimization algorithm for mass minimization with multiple structural constraints

A bidirectional evolutionary structural optimization algorithm is presented, which employs integer linear programming to compute optimal solutions to topology optimization problems with the objective of mass minimization. The objective and constraint functions are linearized using Taylor's first-order approximation, thereby allowing the method to handle all types of constraints without using Lagrange multipliers or sensitivity thresholds. A relaxation of the constraint targets is performed such that only small changes in topology are allowed during a single update, thus ensuring the existence of feasible solutions. A variety of problems are solved, demonstrating the ability of the method to easily handle a number of structural constraints, including compliance, stress, buckling, frequency, and displacement. This is followed by an example with multiple structural constraints and, finally, the method is demonstrated on a wing-box, showing that topology optimization for mass minimization of real-world structures can be considered using the proposed methodology.     

A mass constraint formulation for structural topology optimization with multiphase materials

This work is focused on the topology optimization of lightweight structures consisting of multiphase materials. Instead of adopting the common idea of using volume constraint, a new problem formulation with mass constraint is proposed. Meanwhile, recursive multiphase materials interpolation (RMMI) and uniform multiphase materials interpolation (UMMI) schemes are discussed and compared based on numerical tests and theoretical analysis. It is indicated that the nonlinearity of the mass constraint introduced by RMMI brings numerical difficulties to attain the global optimum of the optimization problem. On the contrary, the UMMI‐2 scheme makes it possible to formulate the mass constraint in a linear form with separable design variables. One such formulation favors very much the problem resolution by means of mathematical programming approaches, especially the convex programming methods. Moreover, numerical analysis indicates that fully uniform initial weighting is beneficial to seek the global optimum when UMMI‐2 scheme is used. Besides, the relationship between the volume constraint and mass constraint is theoretically revealed. The filtering technique is adapted to avoid the checkerboard pattern related to the problem with multiphase materials. Numerical examples show that the UMMI‐2 scheme with fully uniform initial weighting is reliable and efficient to deal with the structural topology optimization with multiphase materials and mass constraint. Meanwhile, the mass constraint formulation is evidently more significant than the volume constraint formulation. Copyright © 2011 John Wiley & Sons, Ltd.     

State update algorithm for isotropic elastoplasticity by incremental energy minimization

An original state update algorithm for the numerical integration of rate independent small strain elastoplastic constitutive models, treating in a unified manner a wide class of yield functions depending on all three stress invariants, is proposed. The algorithm is based on an incremental energy minimization approach, in the framework of generalized standard materials with convex free‐energy and dissipation potential. Under the assumption of isotropic material behavior, implying coaxiality of trial stress, increment of plastic strain, and updated stress, the problem is reduced from dimension six to three. Then, exploiting the cylindrical tensor basis associated with Haigh–Westergaard coordinates, the problem is recast in terms of two nested scalar equations. The proposed algorithm (i) exhibits global convergence even for yield functions with difficult features, such as not being defined on the whole stress space, or implying high‐curvature points of the yield domain, and (ii) requires no matrix inversion. After the tensor reconstruction of the unknowns, a simple expression for the algorithmic consistent material tangent is derived. The algorithm is validated by comparison with benchmark semi‐analytic solutions. Numerical results on single material points and finite element simulations are reported for assessing its accuracy, robustness, and efficiency. A Matlab implementation is provided as supplementary material. Copyright © 2015 John Wiley & Sons, Ltd.     

A new efficient convergence criterion for reducing computational expense in topology optimization: reducible design variable method

A new efficient convergence criterion, named the reducible design variable method (RDVM), is proposed to save computational expense in topology optimization. There are two types of computational costs: one is to calculate the governing equations, and the other is to update the design variables. In conventional topology optimization, the number of design variables is usually fixed during the optimization procedure. Thus, the computational expense linearly increases with respect to the iteration number. Some design variables, however, quickly converge and some other design variables slowly converge. The idea of the proposed method is to adaptively reduce the number of design variables on the basis of the history of each design variable during optimization. Using the RDVM, those design variables that quickly converge are not considered as design variables for the next iterations. This means that the number of design variables can be reduced to save the computational costs of updating design variables. Then, the iteration will repeat until the number of design variables becomes 0. In addition, the proposed method can lead to faster convergence of the optimization procedure, which indeed is a more significant time saving. It is also revealed that the RDVM gives identical optimal solutions as those by conventional methods. We confirmed the numerical efficiency and solution effectiveness of the RDVM with respect to two types of optimization: static linear elastic minimization, and linear vibration problems with the first eigenvalue as the objective function for maximization. Copyright © 2012 John Wiley & Sons, Ltd.     

A new hybrid meta-heuristic algorithm for optimal design of large-scale dome structures

In this article a hybrid algorithm based on a vibrating particles system (VPS) algorithm, multi-design variable configuration (Multi-DVC) cascade optimization, and an upper bound strategy (UBS) is presented for global optimization of large-scale dome truss structures. The new algorithm is called MDVC-UVPS in which the VPS algorithm acts as the main engine of the algorithm. The VPS algorithm is one of the most recent multi-agent meta-heuristic algorithms mimicking the mechanisms of damped free vibration of single degree of freedom systems. In order to handle a large number of variables, cascade sizing optimization utilizing a series of DVCs is used. Moreover, the UBS is utilized to reduce the computational time. Various dome truss examples are studied to demonstrate the effectiveness and robustness of the proposed method, as compared to some existing structural optimization techniques. The results indicate that the MDVC-UVPS technique is a powerful search and optimization method for optimizing structural engineering problems.     

A versatile software tool for microwave planar radar absorbing materials design using global optimization algorithms

A computer-aided design (CAD) tool for the design of planar multi-layer coatings with high absorption for a desired frequency and angle range is presented. The tool uses deterministic and evolutionary optimization design methods. Both single and multi-objective design algorithms can be used and a single absorber design or the Pareto front can be found accordingly. A novel design technique utilizing PSO is also presented. A user-defined or a pre-defined design case can be selected interchangeably. The choice of selecting materials from pre-defined database is also available. The tool can be useful for both educational and research purposes. The efficiency of the tool is demonstrated through several design cases that are in agreement with existing literature data.     

A topological optimization approach for structural design of a high‐speed low‐load mechanism using the equivalent static loads method

In high‐speed low‐load mechanisms, the principal loads are the inertial forces caused by the high accelerations and velocities. Hence, mechanical design should consider lightweight structures to minimize such loads. In this paper, a topological optimization method is presented on the basis of the equivalent static loads method. Finite element (FE) models of the mechanism in different positions are constructed, and the equivalent loads are obtained using flexible multibody dynamics simulation. Kinetic DOFs are used to simulate the motion joints, and a quasi‐static analysis is performed to obtain the structural responses. The element sensitivity is calculated according to the static‐load‐equivalent equilibrium, in such a way that the influence on the inertial force is considered. A dimensionless component sensitivity factor (strain energy caused by unit load divided by kinetic energy from unit velocity) is used, which quantifies the significance of each element. Finally, the topological optimization approach is presented on the basis of the evolutionary structural optimization method, where the objective is to find the maximum ratio of strain energy to kinetic energy. In order to show the efficiency of the presented method, we presented two numerical cases. The results of these analyses show that the presented method is more efficient and can be easily implemented in commercial FE analysis software. Copyright © 2011 John Wiley & Sons, Ltd.