用序列二次规划可以高效率地解决许多工程结构的优化问题。一类问题将原来的非线性规划用力学处理和Taylor展开化为一系列二次规划问题，在目标函数可分离的情况下，通过Kuhn-Tucker条件进一步化为以Lagrange乘子为变量的准无约束的二次规划，在目标函数不可分离情况下，则直接求解原变量的近似二次规划，经过序列迭代，可以求解工程结构的静、动力优化问题。另一类问题是将原问题化为正多项式的几何规划，再将其对偶问题化为二次规划，序列迭代求解之，可以求解目标函数、约束函数非线性程度高的工程问题，对按设计规范公式进行设计的一类问题尤为有效

基于有限元概念，本文研究了结构响应对于设计变量的严格解析解，以空间桁架为例，得到了位移显式的解析表达式——一个关于截面设计变量的有理函数，并进行了严格的数学论证；进而推出了有益于结构敏度分析、结构优化的若干结论，针对含有位移显式的优化模型，提出了采用广义几何规划解法的建议；最后计算了若干简例。

论述了无约束曲线寻优得到局部最优点的结论，研究了约束曲线寻优的近似解析方法，提出近似可分离规划的对偶求解途径，数值实验表明这是一种具有竞争力的解法。

There are three difficulties in the topology optimization problem of continuum structure: (1) The problem under multiple load case is not easy to be approached than one under single load case, because the former becomes a multiple objective problem based on compliance objective function. (2) The problem with local constraints, such as elemental stress limit, is not easy to be solved than one with global constraints, such as displacement or frequency limits, because sensitivity analysis of the former has too expensive computation. (3) The problem with a phenomenon of ill-conditioned load, which is similar with ill-conditioned stiffness matrix in the structural analysis, is not easy to get reasonable final topological structure, because the former is difficult to consider different influences between the loads with small forces and the loads with big forces, and some of topology paths of transferring small forces may disappear during the process of iteration. To overcome above difficulties, five measures are adopted below: (1) Topology optimization model is established by ICM (Independent Continuous Mapping) method. Difficulties caused by multiple objective function of compliance are overcome owing to taking weight as objective function. (2) Based on the von Mises criteria in theory of elastic failure, all element's stress constraints are transformed into a structural energy constraint, namely, a global constraint substitutes for lots of local constraints. (3) To approach of structural energies under multiple load cases, the process of optimization is divided into three steps: <a> the structural energy under the load case corresponding to maximal structural energy subjected to a weight constraint is minimized to converge a minimum energy; <b> according to the minimum energy, a formula based on numerical experience is obtained to determine the allowable structural energy under each load case; <c> an optimization model with the weight function subjected to all allowable structural energies is established and solved to search the optimum topological structure. (4) The phenomenon of the ill-conditioned load is divided to classify into three cases: <a> ill-condition exists between load cases, but not within each load case; <b> ill-condition exists within some load case; <c> ill-condition exists not only between load cases, but also within some load case. (5) A strategy based on strain energy is proposed to adopt ICM method with stress globalization, and the problems of the above mentioned three cases of ill-conditioned load are solved in term of different complementary approaches one by one. Several numerical examples show that the topology path of transferring forces can be obtained more easily by substituting global strain energy constraints for local stresses constraints, and the problem of ill-conditioned load can be solved well by the weighting method which take structural energy as weighting coefficient.

本文在文[4]的基础上，按“有无复合体”模型对应力约束下多工况平面连续体结构拓扑优化的求解进行研究，提出了“工况影响系数”的概念，用于“病态荷载”问题的识别和解决，获得了令人满意的数值结果。

以超静定桁架结构为背景研究了自适应结构的承载能力。 探讨作动器和杆单元的共同工作,用以进行结构分析和控制结构承载能力。 后者意指通过作动器的主动变形调控结构的内力分布以获得更加合理的工作状态。

将ICM（独立、连续、映射）优化方法应用于刚架结构，建立了以重量为目标函数、考虑多工况下应力和位移约束的刚架结构拓扑优化模型。借助于磨光函数和过滤函数，实现了离散变量和连续变量之间的相互转换。考虑多工况应力拓扑解之间、应力和位移约束下拓扑解之间的协调，得到了合理的结果。文中给出的刚架结构拓扑优化算例表明，刚架结构的拓扑结构不同于桁架或连续体。

根据嵌入压电作动器的自适应桁架结构的机电耦合特性，考虑了结构强度、节点最大位移以及作动器最大控制电压等约束条件,提出了以强度、位移和能耗为目标、以电压为控制参数的多目标最优控制模型。该模型通过引入权系数,使多目标问题转化为一个二次目标、线性约束的二次规划问题。限制了设计变量每一步的运动极限，从而保证了算法的稳定性。用数值方法模拟了该模型对结构的控制效果。数值算例表明，该模型具有改善静不定结构应力状态、保证结构形变精度及调节控制能耗的功能。对于静不定结构，可以在一定程度上降低结构的最大工作应力。该模型还具有较小的能耗指标，并使控制点的节点位移尽可能小，利用该模型可以有效地实现单点或多点位移控制。

运用人工神经网络“反向传播”模型，建立神经网络的拓扑结构，设计相应的网络学习算法；将影响套管柱射孔段强度的主要因素作为系统的输入，确定强度影响系数K与诸因素之间的关系，从而得到预测影响系数K的模型。实例分析结果表明模型预测精度高，可靠性强，是一种有效的预测方法。

直径300mm硅片的生产技术是当今硅材料生产研究的重要方向之一，而晶体生长界面的形状、温度分布、晶体中氧的浓度和均匀性等对熔体流动状态十分敏感，采用实验的方法来测量熔体的流动、温度场分布是很困难的，因此很难通过实验的方法获得熔体的流动是如何影响晶体生长的质量的，而数值模拟能提供熔体流动、温度分布等详细内容，为单晶硅的生长提供有利的指导，本文采用低雷诺数的K-ε紊流模型，对直径300mm的大直径单晶硅生长进行了数值模拟，通过熔体在有、无勾形磁场作用时的流场、温度场的分析，阐明了勾形磁场影响熔体流动的机理。