Structural optimization with crashworthiness constraints

An automated structural design methodology has been devised which simultaneously considers design criteria associated with both linear elastic and crashworthiness loading conditions. This method is developed within the context of a nonlinear mathematical programming based structural optimization capability using an efficient two-phased crashworthiness analysis technique. Specially constructed nonlinear approximations for the crashworthiness constraints are employed to further reduce the computational burden during the optimization process. This methodology is demonstrated on an automobile structural design problem. It is shown that more mass efficient designs can be obtained by simultaneously considering elastic and crashworthiness design criteria as compared to a sequential approach in which the structure is first designed for the elastic loads and then modified to satisfy the crashworthiness criteria.     

Structural optimization using probabilistic constraints

In practice, there are often uncertainties associated with material as well as geometric properties, external forces, boundary conditions and operational environment in designing engineering structures. The most common and traditional approach to account for uncertainties is to introduce a factor of safety in the design model. However, such a simplistic solution fails to quantify reliability of the optimum design since a large factor of safety may not imply higher reliability. To directly account for the probabilistic nature of quantities such as material properties, loads, etc., one has to identify and define the respective quantities as random variables in the analysis model. Probability of failure (or reliability) of a structure subject to a performance constraint in the form of a limit state function can then be calculated and formulated as a constraint in the design optimization model. Probabilistic constraint formulation for explicit limit state functions is presented in this paper. Due to this formulation, probabilistic constraints can now be considered routinely in a structural optimization software with additional computational costs. Results for a representative set of structural and mechanical design problems are presented to validate the probabilistic constraint formulation. With the introduction of reliability based constraints, the optimized structure tends to be insensitive to fabrication defects and improper definition of the loading environment.Nomenclature X a vector of design variables,X _i - Y a vector of random variables,Y _i - g(X, Y) limit state function - P _f orP probability of failure - R reliability = (1 –P _f) - H.O.T. higher order terms - mean value - standard normal cumulative distribution function - u standard normal variable - reliability index - unsafe region     

Structural topology optimization with constraints on multi-fastener joint loads

This paper addresses an important problem of design constraints on fastener joint loads that are well recognized in the design of assembled aircraft structures. To avoid the failure of fastener joints, standard topology optimization is extended not only to minimize the structural compliance but also to control shear loads intensities over fasteners. It is shown that the underlying design scheme is to ameliorate the stiffness distribution over the structure in accordance with the control of load distributions over fastener joints. Typical examples are studied by means of topology optimization with joint load constraints and the standard compliance design. The effects of joint load constraints are highlighted by comparing numerical optimization results obtained by both methods. Meanwhile, resin models of optimized designs are fabricated by rapid prototyping process for loading test experiments to make sure the effectiveness of the proposed method.     

Accurate CFD driven optimization of lifting surfaces for wing-body configuration

A robust and accurate method for the multipoint CFD driven constrained optimization of 2D airfoils for minimum drag, previously developed by the authors, is extended to the optimization of 3D lifting surfaces for wing-body aircraft configurations. The objective is to minimize total drag at fixed lift subject to numerous geometrical and aerodynamical constraints. The optimization method is based on the use of Genetic Algorithms, accurate full Navier-Stokes drag prediction and massive multilevel parallelization of the whole computational framework. The method was applied to the problem of multipoint optimization of wings incorporated into transport-type aircraft configurations, by the example of ARA M-100 wing-body shape (a NASA test case). For the considered class of problems, significant aerodynamic gains have been obtained.     

Structural optimization by displaying the reliability constraints

This paper presents an approach for structural optimization design by means of displaying the reliability constraints. To begin with, a variety of non-normal random loads to which the structure is subjected are transformed into normal types of loads by means of normal tail transformation. Then the reliability constraints, namely displacement and stress, are transformed into constraints of conventional forms according to the characteristics of invariance in a linear elastic structures to the normal loads. At the end, the problem of reliabliltiy optimization is solved by the mixed method and satisfactory results have been obtained.     

基于粒子群优化的有约束模型预测控制器

研究了模型预测控制(MPC)中解决带约束的优化问题时所用到的优化算法,针对传统的二次规划(QP)方法的不足,引入了一种带有混沌初始化的粒子群优化算法(CPSO),将其应用到模型预测控制中,用十解决同时带有输入约束和状态约束的控制问题.最后,引入了一个实际的带有约束的线性离散系统的优化控制问题,分别用二次规划和粒子群优化两种算法去解决,通过仿真结果的比较,说明了基于粒子群优化(PSO)的模型预测控制算法的优越性.     

Run-to-run optimization via control of generalized constraints

Run-to-run optimization methodologies exploit the repetitive nature of batch processes to determine the optimal operating policy in the presence of uncertainty. In this paper, a parsimonious parameterization of the inputs is used and the decision variables of the parameterization are updated on a run-to-run basis using a feedback control scheme which tracks signals that are invariant under uncertainty. In this run-to-run framework, terminal constraints of the optimization problem and cost sensitivities constitute the invariant signals. The methodology is conceived to improve the cost function from batch-to-batch without constraint violation.     

Structural optimization on geometrical configuration and element sizing with statical and dynamical constraints

In this paper, a bi-factor -β algorithm based on the Kuhn-Tucker criteria about the minimal weight design of a structure under statical and dynamical constraints, is presented. Among the constraints, that of “frequency-prohibited band” is a new formulation which requires any characteristic frequency of the structure not to fall into a certain frequency region. The desing variables may cover sizes of the elements and/or coordinates of the nodes. The upper and lower bounds of each variable are specified, and the stress constraints based on full-stress criteria may also be taken into account. Satisfactory results have been obtained over varous examples wherein the stiffness and/or mass matrices of the structure may be highly nonlinear about the design variables.     

Boolean surfaces with shape constraints

In this paper, we present a new method for the construction of parametric surfaces reproducing an object from a set of spatial data. We adopt a hybrid scheme, based on the Boolean sum of variable degree spline operators, which both interpolate a set of grid lines and approximate the data. As usual the variable degrees can be chosen to satisfy proper shape constraints.     

Periodic optimization of linear systems under control power constraints

The periodic optimization problem of maximizing the output power of a linear system under a control power constraint is analyzed in this paper. The explicit form of the optimal solution is found by means of a frequency domain approach.     

基于混沌粒子群优化的约束状态反馈预测控制算法

提出一种基于混沌粒子群优化的约束状态反馈预测控制算法,用于解决带有输入约束和状态约束的控制问题.将混沌粒子群优化引入到约束状态反馈预测控制的滚动优化过程中,增强了算法在约束范围内的局部搜索和全局搜索能力.通过对一个实际的带有约束的线性离散系统控制优化问题的解决,验证了基于混沌粒子群优化的状态反馈预测控制算法的可行性和有效性,与传统的二次规划算法的比较结果说明了此算法的优越性,证明了状态反馈预测控制系统良好的鲁棒性.     

Structural optimization with fatigue and ultimate limit constraints of jacket structures for large offshore wind turbines

The purpose of the research presented in this paper is to develop and implement an efficient method for analytical gradient-based sizing optimization of a support structure for offshore wind turbines. In the jacket structure optimization of frame member diameter and thickness, both fatigue limit state, ultimate limit state, and frequency constraints are included. The established framework is demonstrated on the OC4 reference jacket with the NREL 5 MW reference wind turbine installed at a deep water site. The jacket is modeled using 3D Timoshenko beam elements. The aero-servo-elastic loads are determined using the multibody software HAWC2, and the wave loads are determined using the Morison equation. Analytical sensitivities are found using both the direct differentiation method and the adjoint method. An effective formulation of the fatigue gradients makes the amount of adjoint problems that needs to be solved independent of the amount of load cycles included in the analysis. Thus, a large amount of time-history loads can be applied in the fatigue analysis, resulting in a good representation of the accumulated fatigue damage. A reduction of 40 % mass is achieved in 23 iterations using the CPLEX optimizer by IBM ILOG, where both fatigue and ultimate limit state constraints are active at the optimum.     

Structural optimization with design constraints on peak responses to temporally correlated quasi-static load processes

Structural and Multidisciplinary Optimization - Structural optimization has become a widely used tool for various applications due to its capability of providing design freedom and promise to...     

Texture mapping subdivision surfaces with hard constraints

We propose a texture mapping technique that allows user to directly manipulate texture coordinates of subdivision surfaces through adding feature correspondences. After features, or constraints, are specified by user on the subdivision surface, the constraints are projected back to the control mesh and a polygon matching/embedding algorithm is performed to generate polygon regions that embed texture coordinates of control mesh into different regions. After this step, some Steiner points are added to the control mesh. The generated texture coordinates exactly satisfy the input constraints but with high distortions. Then a constrained smoothing algorithm is performed to minimize distortions of the subdivision surface via updating texture coordinates of the control mesh. Finally, an Iterative Closest Point (ICP)-based deformation algorithm is performed to remove subdivision errors caused by the added Steiner points.     

曲线插值约束的LOOP细分曲面

提出基于Loop细分方法的曲线插值方法,不需要修改细分规则,只需以插值曲线的控制多边形为中心多边形,向其两侧构造对称三角网格带,该对称三角网格带将收敛于插值曲线。因此,包含有该三角网格带的多面体网格的极限曲面将经过插值曲线。若要插值多条相交曲线只需在交点处构造全对称三角网格。运用该方法可在三角网格生成的细分曲面中插值多达六条的相交曲线。     

带状态约束的非线性系统单向辅助面滑模控制

针对带有状态输出有界约束的一类不确定仿射非线性系统,提出一种单向辅助面滑模控制器设计方法．该方法通过将状态量的约束条件引入单向辅助面的设计,并利用单向辅助面构成系统状态输出量正不变集的边界,以保证系统状态能够满足状态输出量的约束条件．随后给出了该方法稳定性以及单向辅助面构成正不变集的理论证明,并通过仿真验证了所提出的设计方法的有效性．     

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...