Truss layout optimization within a continuum

The present work extends truss layout optimization by considering the case when it is embedded in a continuum. Structural models often combine discrete and continuum members and current requirements for efficiency and extreme structures push research in the field of optimization. Examples of varied complexity and dimensional space are analyzed and compared, highlighting the advantages of the proposed method. The goal of this work is to provide a simple formulation for the discrete component of the structure, more specifically the truss, to be optimized in presence of a continuum.     

空间桁架结构优化设计

为获得空间桁架结构的合理构型,以某空间设备支撑结构为例,分析结构材料在设计空间的分布形式和桁架结构的传力路径。在已知载荷约束和设计空间大小的条件下,基于连续体拓扑优化方法,以静态多工况刚度和动态固有频率为多目标函数进行优化分析。依据设计要求确定计算模型的结点数和结点位置,获得满足要求的空间桁架结构并进行优化设计。优化结果比原模型质量减少36.7%,一阶模态提高3.6%。     

Dynamic response of trussed bridges for moving loads

A continuum approach is presented to obtain the transverse vibration of trussed bridges traversed by a single moving load. The efficiency and the accuracy of the method are determined by comparing its results with those obtained by the dynamic analysis of the bridge as a discrete lumped mass system, which can account for both truss action and flexural action of the deck in the response. Using the proposed method, a parametric study is performed to show the influence of some important parameters on the dynamic response of the bridge. The parameters include relative stiffness of the bridge deck and truss, number of panels, type of truss and speed parameter.     

空间桁架的人-机协作装配规划与试验验证

该文以空间直立桁架结构的人-机协作装配流程为研究对象,提出一种适用于径向快装桁架模块单元的创新构型,建立了基于状态矩阵和邻接矩阵的桁架结构装配序列、装配模式和装配过程的数学模型。该文还对空间环境下桁架装配的人-机能力约束进行分析,提出基于动素分析的装配任务层级化分解方法,利用比较分配原则制定了适用编程的人-机协作装配任务流程和分配方案。基于所提出方案,通过开展人穿戴模拟宇航服与机械臂协作装配 5 m 长直立桁架结构的地面演示试验,验证了该方案的合理性和组装流程的可行性,为空间大型设施在轨构建提供了技术原理支撑。     

考虑间隙运动副的桁架单胞等效建模与分析

本文主要研究了含间隙运动副桁架单胞的等效建模方法.主要考虑了桁架单胞的等效刚度问题以及阻尼问题.首先从间隙铰链开始研究,提出全面的铰链模型;其次提出用位移法将桁架单胞等效成板,即把桁架单胞看成是由梁元组成的钢架结构,运用平面钢架位移法得出桁架单胞的等效刚度矩阵,进而得出结构的整体固有频率和等效后的板的刚度矩阵.最后用有限元软件ANSYS对单胞结构在不同边界条件下进行了模态分析,将在自由边界条件下的固有频率和解析得出的频率做了对比,发现二者有很好的吻合度.结果表明由于间隙运动副的存在,使得桁架单胞结构的刚度降低,柔性增强.     

Elastoplastic truss design using a displacement based optimization

A displacement based optimization (DBO) method is applied to truss design problems with material nonlinearities, to explore feasibility and verify efficiency of the method as compared to traditional structural optimization. Minimum-weight truss sizing problems with various path-independent elastoplastic laws, including elastic perfectly plastic, linear strain hardening, and Ramberg–Osgood models, are investigated. This type of material nonlinearity allows us to naturally extend the linear elastic truss sizing in the DBO setting to nonlinear problems. To implement the methodology a computer program that uses the commercially available optimizer DOT by VR&D and IMSL Linear Programming solver by Visual Numerics is developed. Several test problems are successfully solved using the DBO approach and solutions are compared to those available in the literature, demonstrating significant reduction of computational time in comparison to the traditional structural optimization method. In particular, the DBO approach is found to be suitable for truss topology design since the method allows member areas to have cross-sectional areas equal to zero exactly.     

Porous structure design through Blinn transformation-based level set method

This paper presents a novel porous structure modeling and shape optimization method. Specifically, the porous structure is simplified into a truss network, and the connecting node positions are optimized to achieve the optimal stiffness. Simultaneously, the porosity distribution is tailored by adding local geometry control constraints. Then, as a following step, the truss elements are restored back into the explicit form, described by the parametric level set functions; and by conducting the Blinn transformation, the optimized truss structure is transformed into a continuum lattice model with smooth transitions at the internal joints. Finally, the maximum stress level at the joints is optimized through parametric level set shape optimization. In summary, this method is effective in building heterogeneous porous structures with tailored porosity distribution, and more importantly, both the stiffness and the stress level can be effectively optimized, which is an outstanding characteristic compared to the majority of the existing porous structure modeling and optimization methods. Effectiveness of the proposed method is proved through a few numerical case studies.

     

Computing Equilibrium Wealth Distributions in Models with Heterogeneous-Agents, Incomplete Markets and Idiosyncratic Risk

This paper describes an accurate, fast and robust fixed point method for computing the stationary wealth distributions in macroeconomic models with a continuum of infinitely-lived households who face idiosyncratic shocks with aggregate certainty. The household wealth evolution is modeled as a mixture Markov process and the stationary wealth distributions are obtained using eigen structures of transition matrices by enforcing the conditions for the Perron–Frobenius theorem by adding a perturbation constant to the Markov transition matrix. This step is utilized repeatedly within a binary search algorithm to find the equilibrium state of the system. The algorithm suggests an efficient and reliable framework for studying dynamic stochastic general equilibrium models with heterogeneous agents.     

Optimal configuration for the self-identification of a two-dimensional variable geometry truss

This study addresses the optimal changes in geometry of a two-dimensional variable geometry truss (VGT) to identify the stiffness matrix of the truss using the concept of self-identification. The optimization of the geometry changing of the VGT is a problem of selecting the optimal combination of multiple design variables from a large number of candidate sets. This study proposes a simple optimization method for determining a set of optimal geometric parameters; in this method, the approximated mode shape matrix obtained using spline interpolation techniques is used to calculate the objective function for self-identification. The objective function used in this paper is a function of the condition number of the coefficient matrix of a linear matrix equation and a criterion for self-identification. The proposed algorithm can be used to reduce the number of actual vibration tests required for measuring the mode shapes and modal frequency while it maximizes the objective function. Numerical experiments are conducted to investigate the relationship between the convergence characteristics of the optimization and the target vibration modes. The effectiveness of the optimized geometry changing is verified by comparing the identification error for the uniform geometry changing, the optimized one for the three lower modes of the VGT, and the one found by a classical QR decomposition. Furthermore, the numerical results show that the identification sensitivity with respect to noisy data is reduced by the optimization.     

An iterative solution for geometrically nonlinear trusses

Successive applications of the stiffness method were used to analyze geometrically nonlinear space trusses. Each cycle consists of the computation of corrective displacements using a revised stiffness matrix subjected to a residule load vector. The stiffness matrix is based upon the displaced geometry of the structure. The residule load vector is obtained by computing the differences between the applied loads and the components of bar forces at each joint. These force components are based upon the displaced joint locations.A computer program based upon this method was developed and applied to several small plane trusses and a large transmission tower space truss. The method was found to converge rapidly in the cases investigated. Comparisons with the piece-wise linear method are presented, indicating some important advantages to the iterative approach.     

A simplified finite element solution for the plates on elastic foundation

The simplified Finite Element Method is used to analyze plates supported on an elastic continuum. The method assembles the stiffness matrix of the foundation into a banded, diagonal matrix and, therefore, can be solved by using the tridiagonal technique. This process reduces the computer storage dramatically. Various problems of plates on elastic continua have been solved and the results are compared with those obtained using the conventional Finite Element Methods. Good agreements are obtained.     

A general boundary approach to the construction of Michell truss structures

The goal of the present study is to provide a building block approach which will enable the synthesis of new Michell truss structure solutions. Curved support boundaries for Michell truss structures are categorized into four types. Each type is graphically illustrated as a simple example structure. A general matrix operator method is developed to solve the layout of each type. Numerical solutions that use the matrix method are compared with analytical solutions in a case study that comprises complimentary logarithmic spirals on a circular arc boundary. To illustrate the applications of this study, numerical layout solutions on a circular support boundary are explored that produce a family of globally-optimal Michell cantilever solutions for the support of a distributed load along a straight cantilever flange.     

Shape design sensitivity analysis and optimization of spatially rotating objects

Shape design sensitivity analysis (DSA) and optimization of spatially rotating objects is presented in this paper. Design sensitivity expressions are derived using a continuum DSA method for spatial objects rotating with angular velocity and angular acceleration, based on three definitions of the finite element mass matrix: consistent, lumped, and diagonalized. The design sensitivity expression derived using a diagonalized element mass matrix, which is consistent with the finite element analysis (FEA) method used in ANSYS, is implemented, although the method can work with other FEA codes, such as MSC/NASTRAN or ABAQUS. Since the continuum DSA method is used, sensitivity information can be computed outside the FEA codes by postprocessing finite element data. Rotating block and turbine blade examples are presented to validate the proposed DSA method. The turbine blade example is optimized using an integrated optimization module of the Design Sensitivity Analysis and Optimization (DSO) tool developed at the University of Iowa. The integrated module consists of ANSYS, MSC/NASTRAN, or ABAQUS for FEA; Design Optimization Tool (DOT) for nonlinear programming; and DSA and design model update programs developed in DSO.     

Topology optimization of truss-like continua with three families of members model under stress constraints

A method to minimize structural volume under stress constraints subject to multiple load cases is presented. A new material model is developed and employed to simulate the constitutive relation of the truss-like continuum. It is assumed that there are infinite numbers of members with infinitesimal spaces along three orientations at any position. The densities and orientations of members at all nodes are taken as design variables. An iterative optimization method is presented. In one iteration step, design variables are optimized separately and independently. The orientations of three families of members at every node are optimized by mathematics program method. Fully stressed criterion is adapted to optimize member densities. In the every iteration step, member densities are adjusted to make their strains smaller than the permissible values while the stress states is assumed to keep unchanged. The densities and orientations of members at any point inside an element are obtained by their interpolating the corresponding values (i.e., the densities and orientations) at the nodes of the element. These values vary continuously inside an element and the intermediate values are not suppressed. By using this technique the optimal truss-like continuum is formed, which represents for member distribution field. Once parts of members are chosen, discrete truss can be constructed according to the continuous member distributive field. This discrete structure is a nearly optimal structure. In above process, there are no numerical instabilities such as checkerboard and mesh-dependency. Numerical examples are presented to demonstrate the effectiveness of the present method.     

管桁架设计软件开发

针对管桁架设计过程中绘图工作量大、出错率高、效率低等问题,利用．Net和ObjectARX在AutoCAD 2004中实现管桁架结构设计软件．介绍开发该软件的总体思路、构架和数据存储及基本功能．该软件将三维实体模型应用到管桁架后处理系统之中,通过对实体模型消隐来出图,可以大大减少人工绘图的工作量．     

Dynamic analysis of wind-excited truss tower with friction dampers

This paper presents a rational analytical method for determining dynamic response of wind-excited large truss towers installed with friction dampers and investigates the effectiveness of friction dampers. The analytical procedure involves two models of one truss tower: one is the two-dimensional lumped mass dynamic model and the other is the three-dimensional (3D) finite element static model. These two models are alternately used to fulfill control force transformation, displacement increment transformation, and the numerical integration of equations of motion of the coupled damper-tower system. A three-story truss structure under wind excitation is used to validate the proposed bi-model method through the comparison with a precise 3D dynamic analysis. After a satisfactory comparison, a large space steel television tower is used as an application to examine the feasibility of the bi-model method and the effectiveness of friction dampers. The case study shows that the bi-model method can efficiently compute wind-induced response of the large space television tower with friction dampers and the installation of the friction dampers of proper parameters can significantly reduce wind-induced vibration of the tower.     

Fuzzy multiobjective optimization of truss-structures using genetic algorithm

In this paper, a method for solving fuzzy multiobjective optimization of space truss with a genetic algorithm is proposed. This method enables a flexible method for optimal system design by applying fuzzy objectives and fuzzy constraints. The displacement, tensile stress, fuzzy sets, membership functions and minimum size constraints are considered in formulation of the design problem. An algorithm was developed by using MATLAB programming. The algorithm is illustrated on 56-bar space truss system design problem and the results are discussed.     

On the extension of goal-oriented error estimation and hierarchical modeling to discrete lattice models

The Goals algorithm for adaptive modeling is extended to the case of discrete models such as those characterized by lattice structures (or the static behavior molecular systems) by using surrogate models obtained from continuum approximations of the lattice. The result is a technique that could provide for scale-bridging between continuum models and atomistic models, although the present development concerns only simple algebraic systems. An example is provided in which quantities of interest in system with a large number of degrees of freedom are computed to a preset tolerance in relatively few low-order approximations.