考虑瞬态响应的薄板结构阻尼材料层拓扑优化

讨论了敷设阻尼材料的薄板结构考虑瞬态响应时阻尼材料层的最优布局问题。基于SIMP方法构造人工阻尼材料惩罚模型和结构拓扑优化模型,以阻尼材料的相对密度作为设计变量,在给定阻尼材料用量的条件下,最小化结构瞬态位移响应的时间积分。由于结构整体呈现非比例阻尼特性,采用逐步积分法对结构的振动方程进行求解。通过伴随变量法得到目标函数对设计变量的灵敏度表达式,在此基础上采用基于梯度的移动渐近线方法求解。数值算例验证了优化模型与算法的合理性和有效性。     

结构可靠性优化求解的解耦融合策略

在工程结构的可靠性优化过程中,求解的效率和精度是优化方法的关键。该文提出一种针对解耦优化的融合策略。所提方法在优化迭代解耦所用的失效概率函数为前几次迭代设计点构建的局部失效概率函数的加权融合形式。在对原可靠性优化问题进行解耦后,结合序列近似优化方法进行迭代求解。相比于常规的仅使用当次局部建立的失效概率函数而言,所提融合策略最大限度利用了各次迭代中产生的信息用于优化解耦求解,能够提高失效概率函数的近似精度,从而间接达到减少迭代次数和计算量的目的。最后给出了屋架和十杆结构的可靠性优化算例,验证该文方法的正确性和可行性。     

Computation of pareto optima in structural design

The structural design problem is acknowledge to be commonly multi-criteria in nature. The various bases for multi-criteria optimization methodologies are outlined and a computationally viable method for generating Pareto optimal solutions is adopted for the structural design problem where the criteria may be non-commensurable. A numerical example on optimal truss design illustrating non-commensurable criteria is given.     

On structural shape optimization using an embedding domain discretization technique

This contribution presents a novel approach to structural shape optimization that relies on an embedding domain discretization technique. The evolving shape design is embedded within a uniform finite element background mesh which is then used for the solution of the physical state problem throughout the course of the optimization. We consider a boundary tracking procedure based on adaptive mesh refinement to separate between interior elements, exterior elements, and elements intersected by the physical domain boundary. A selective domain integration procedure is employed to account for the geometric mismatch between the uniform embedding domain discretization and the evolving structural component. Thereby, we avoid the need to provide a finite element mesh that conforms to the structural component for every design iteration, as it is the case for a standard Lagrangian approach to structural shape optimization. Still, we adopt an explicit shape parametrization that allows for a direct manipulation of boundary vertices for the design evolution process. In order to avoid irregular and impracticable design updates, we consider a geometric regularization technique to render feasible descent directions for the course of the optimization. Copyright © 2016 John Wiley & Sons, Ltd.     

基于等几何裁剪分析的拓扑与形状集成优化

提出了将设计和分析、拓扑与形状优化集成的思想,探索了基于等几何裁剪分析的拓扑与形状集成优化设计算法,该方法统一了结构优化的计算机辅助设计、计算机辅助工程分析和优化设计的模型,基于B样条的等几何裁剪分析既能准确表达几何形状,又可以用裁剪面分析方便处理任意复杂拓扑优化问题,由裁剪选择标准确定合理的拓扑结构变动方向,结构变动时无需重新划分网格,设计结果突破初始设计空间的限制,还可方便优化形状。建立了等几何裁剪灵敏度分析的计算方法,给出了等几何裁剪分析拓扑与形状集成优化算法,通过典型实例表明所用方法的正确性和有效性。     

Structural optimization of non-linear systems under stochastic excitation

This work concentrates on the structural optimization of a class of non-linear systems with deterministic structural parameters subject to stochastic excitation. The optimization problem is formulated as the minimization of an objective function subject to constraints on the response level. The stochastic response is characterized by its first two statistical moments, which are computed by a statistical equivalent linearization technique. The implicit structural optimization problem is replaced by a sequence of explicit sub-optimization problems. The sub-problems are constructed by using a conservative first-order approximation of the objective and constraint functions. The applicability of the proposed design process is demonstrated in three numerical examples where the methodology is applied to systems with nonlinearity of hardening and hysteretic type. The effects of the nonlinearity on the general performance of the final designs are discussed. At the same time, some engineering implications of the results obtained in this work are addressed.     

Topology optimization of structures under multiple loading cases with a new compliance–volume product

This article proposes a new topology optimization method for the design of structures under multiple loading cases. The design is formulated as a multi-objective optimization problem by minimizing a new compliance–volume product, which optimizes the overall stiffness and volume simultaneously to avoid the empirical decision on design constraints and obtain an even lower structural volume. A normalized exponential weighted criterion (NEWC) method is included in the multi-objective optimization problem for the capture of the entire Pareto frontier. A weight evaluation method, in terms of the fuzzy multiple-attribute group decision-making (FMAGDM) theory, is incorporated in the problem to evaluate the weights of the objectives and guarantee the optimal design in an acceptable level. The solid isotropic material with penalty (SIMP) method is used to represent the dependence of elemental densities on material properties. Three typical numerical examples are employed to show the effectiveness of the proposed method.     

OPTIMUM SHAPE DESIGN AND POSITIONING OF FEATURES USING THE BOUNDARY INTEGRAL EQUATION METHOD

A design optimization procedure is developed using the boundary integral equation (BIE) method for linear elastostatic two-dimensional domains. Optimal shape design problems are treated where design variables are geometric parameters such as the positions and sizing dimensions of entire features on a component or structure. A fully analytical approach is adopted for the design sensitivity analysis where the BIE is implicitly differentiated. The ability to evaluate response sensitivity derivatives with respect to design variables such as feature positions is achieved through the definition of appropriate design velocity fields for these variables. How the advantages of the BIE method are amplified when extended to sensitivity analysis for this category of shape design problems is also highlighted. A mathematical programming approach with the penalty function method is used for solving the overall optimization problem. The procedure is applied to three example problems to demonstrate the optimum positioning of holes and optimization of radial dimensions of circular arcs on structures.     

Minimum cost design of framed structures by the mini-max dual method

Minimum cost design of a framed structure is considered by using the mini-mas dual method. Stress and/or displacement constraints are imposed as behavioural constraints. The minimum cost design problem has a discrete objective function and discrete design variables. A sequence of approximate optimization problems in created by using the first-order Taylor series expansion for displacements with respect to the reciprocals of cross-sectional areas and moments of inertia. Each approximate problem is solved in the dual space. Two simple structural examples are given to show the appropriateness and efficiency of the proposed procedure. Approximate solutions are obtained within five structural analysis.     

Structural optimization of uncertain dynamical systems considering mixed-design variables

In this paper attention is directed to the reliability-based optimization of uncertain structural systems under stochastic excitation involving discrete-continuous sizing type of design variables. The reliability-based optimization problem is formulated as the minimization of an objective function subject to multiple reliability constraints. The probability that design conditions are satisfied within a given time interval is used as a measure of system reliability. The problem is solved by a sequential approximate optimization strategy cast into the framework of conservative convex and separable approximations. To this end, the objective function and the reliability constraints are approximated by using a hybrid form of linear, reciprocal and quadratic approximations. The approximations are combined with an effective sensitivity analysis of the reliability constraints in order to generate explicit expressions of the constraints in terms of the design variables. The explicit approximate sub-optimization problems are solved by an appropriate discrete optimization technique. The optimization scheme exhibits monotonic convergence properties. Two numerical examples showing the effectiveness of the approach reported herein are presented.     

Simultaneous nonlinear structural analysis and design

Optimization techniques are increasingly being used for performing nonlinear structural analysis. Under these circumstances the structural design problem can be viewed as a nested optimization problem. The present paper suggests that there are computational benefits to treating this nested problem as a large single optimization problem. That is, the response variables (such as displacements) and the structural parameters are all treated as design variables in a unified formulation which performs simultaneously the design and analysis. Three truss examples are used for the demonstration comparing two nested optimization procedures with two computational procedures for the simultaneous solution. The examples show that the simultaneous approach is competitive with the more traditional nested approach.     

Evolutionary Algorithm Integrating Stress Heuristics for Truss Optimization

The optimal truss design using problem-oriented evolutionary algorithm is presented in the paper. The minimum weight structures subjected to stress and displacement constraints are searched. The discrete design variables are areas of members, selected from catalogues of available sections. The integration of the problem specific knowledge into the optimization procedure is proposed. The heuristic rules based on the concept of fully stressed design are introduced through special genetic operators, which use the information concerning the stress distribution of structural members. Moreover, approximated solutions obtained by deterministic, sequential discrete optimization methods are inserted into the initial population. The obtained hybrid evolutionary algorithm is specialized for truss design. Benchmark problems are calculated in numerical examples. The knowledge about the problem integrated into the evolutionary algorithm can enhance considerably the effectiveness of the approach and improve significantly the convergence rate and the quality of the results. The advantages and drawbacks of the proposed method are discussed.     

Crashworthiness design optimization using successive response surface approximations

 Finite Element (FE) method is among the most powerful tools for crash analysis and simulation. Crashworthiness design of structural members requires repetitive and iterative application of FE simulation. This paper presents a crashworthiness design optimization methodology based on efficient and effective integration of optimization methods, FE simulations, and approximation methods. Optimization methods, although effective in general in solving structural design problems, loose their power in crashworthiness design. Objective and constraint functions in crashworthiness optimization problems are often non-smooth and highly non-linear in terms of design variables and follow from a computationally costly (FE) simulation. In this paper, a sequential approximate optimization method is utilized to deal with both the high computational cost and the non-smooth character. Crashworthiness optimization problem is divided into a series of simpler sub-problems, which are generated using approximations of objective and constraint functions. Approximations are constructed by using statistical model building technique, Response Surface Methodology (RSM) and a Genetic algorithm. The approximate optimization method is applied to solve crashworthiness design problems. These include a cylinder, a simplified vehicle and New Jersey concrete barrier optimization. The results demonstrate that the method is efficient and effective in solving crashworthiness design optimization problems. Received: 30 January 2002 / Accepted: 12 July 2002 Sponsorship for this research by the Federal Highway Administration of US Department of Transportation is gratefully acknowledged. Dr. Nielen Stander at Livermore Software Technology Corporation is also gratefully acknowledged for providing subroutines to create D-optimal experimental designs and the simplified vehicle model.     

THE ROLE OF EVOLUTIONARY AND ADAPTIVE SEARCH DURING WHOLE SYSTEM,CONSTRAINED AND DETAILED DESIGN OPTIMIZATION

The paper introduces various strategies which incorporate evolutionary and adaptive search techniques. These strategies incorporate genetic algorithms (GA) and ant colony models combined within co-operating frameworks that provide a capability for decision support and optimization during whole system design and constraint satisfaction/ constrained optimization during the engineering design process. The objective during whole system design is to determine an optimum initial configuration for large engineering systems. Strategies for the efficient integration of evolutionary techniques with detailed design are also introduced. Each of these areas presents specific problems to the evolutionary/adaptive search processes and the overall objective here is to identify the main areas of difficulty and provide solutions that will lead to successful integration. The paper illustrates the flexibility and utility of the various techniques when applied across the various stages of the design process, i.e. from providing decision support during the high-risk stages of preliminary design to the identification of definitive optimal solutions during the more deterministic stages of detailed design.     

Implementation of Discrete Capability into the Enhanced Multipoint Approximation Method for Solving Mixed Integer-Continuous Optimization Problems

Multipoint approximation method (MAM) focuses on the development of metamodels for the objective and constraint functions in solving a mid-range optimization problem within a trust region. To develop an optimization technique applicable to mixed integer-continuous design optimization problems in which the objective and constraint functions are computationally expensive and could be impossible to evaluate at some combinations of design variables, a simple and efficient algorithm, coordinate search, is implemented in the MAM. This discrete optimization capability is examined by the well established benchmark problem and its effectiveness is also evaluated as the discreteness interval for discrete design variables is increased from 0.2 to 1. Furthermore, an application to the optimization of a lattice composite fuselage structure where one of design variables (number of helical ribs) is integer is also presented to demonstrate the efficiency of this capability.     

Isogeometric topology optimization for continuum structures using density distribution function

This paper will propose a more effective and efficient topology optimization method based on isogeometric analysis, termed as isogeometric topology optimization (ITO), for continuum structures using an enhanced density distribution function (DDF). The construction of the DDF involves two steps. (1)  Smoothness: the Shepard function is firstly utilized to improve the overall smoothness of nodal densities. Each nodal density is assigned to a control point of the geometry. (2) Continuity: the high-order NURBS basis functions are linearly combined with the smoothed nodal densities to construct the DDF for the design domain. The nonnegativity, partition of unity, and restricted bounds [0, 1] of both the Shepard function and NURBS basis functions can guarantee the physical meaning of material densities in the design. A topology optimization formulation to minimize the structural mean compliance is developed based on the DDF and isogeometric analysis to solve structural responses. An integration of the geometry parameterization and numerical analysis can offer the unique benefits for the optimization. Several 2D and 3D numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed ITO method, and the optimized 3D designs are prototyped using the Selective Laser Sintering technique.     

Multimaterial topology design for optimal elastic and thermal response with material-specific temperature constraints

We present an original method for multimaterial topology optimization with elastic and thermal response considerations. The material distribution is represented parametrically using a formulation in which finite element–style shape functions are used to determine the local material properties within each finite element. We optimize a multifunctional structure that is designed for a combination of structural stiffness and thermal insulation. We conduct parallel uncoupled finite element analyses to simulate the elastic and thermal response of the structure by solving the two-dimensional Poisson problem. We explore multiple optimization problem formulations, including structural design for minimum compliance subject to local temperature constraints so that the optimized design serves as both a support structure and a thermal insulator. We also derive and implement an original multimaterial aggregation function that allows the designer to simultaneously enforce separate maximum temperature thresholds based upon the melting point of the various design materials. The nonlinear programming problem is solved using gradient-based optimization with adjoint sensitivity analysis. We present results for a series of two-dimensional example problems. The results demonstrate that the proposed algorithm consistently converges to feasible multimaterial designs with the desired elastic and thermal performance.     

An asymmetric suboptimization approach to aerostructural optimization

An asymmetric suboptimization method for performing multidisciplinary design optimization is introduced. The objective of the proposed method is to improve the overall efficiency of aerostructural optimization, by simplifying the system-level problem, and thereby reducing the number of calls to a potentially costly aerodynamics solver. To guide a gradient-based optimization algorithm, an extension of the coupled sensitivity equations is developed to include post-optimality information from the structural suboptimization. The optimization of an aircraft wing is performed using linear aerodynamic and structural analyses, and a thorough performance comparison is made between the new approach and the conventional multidisciplinary feasible method. The asymmetric suboptimization method is found to be the more efficient approach when it adequately simplifies the system-level problem, or when there is a large enough discrepancy between disciplinary solution times. I.R. Chittick is graduate student. J.R.R.A. Martins is assistant Professor.     

Simultaneous optimal design of structural topology, actuator locations and control parameters for a plate structure

 Simultaneous optimization with respect to the structural topology, actuator locations and control parameters of an actively controlled plate structure is investigated in this paper. The system consists of a clamped-free plate, a H ₂ controller and four surface-bonded piezoelectric actuators utilized for suppressing the bending and torsional vibrations induced by external disturbances. The plate is represented by a rectangular design domain which is discretized by a regular finite element mesh and for each element the parameter indicating the presence or absence of material is used as a topology design variable. Due to the unavailability of large-scale 0–1 optimization algorithms, the binary variables of the original topology design problem are relaxed so that they can take all values between 0 and 1. The popular techniques in the topology optimization area including penalization, filtering and perimeter restriction are also used to suppress numerical problems such as intermediate thickness, checkerboards, and mesh dependence. Moreover, since it is not efficient to treat the structural and control design variables equally within the same framework, a nested solving approach is adopted in which the controller syntheses are considered as sub processes included in the main optimization process dealing with the structural topology and actuator locations. The structural and actuator variables are solved in the main optimization by the method of moving asymptotes, while the control parameters are designed in the sub optimization processes by solving the Ricatti equations. Numerical examples show that the approach used in this paper can produce systems with clear structural topology and high control performance. Received 16 November 2001 / Accepted 26 February 2002