基于矢量合成的可行方向法

针对可行方向法中，搜索可用的可行方向这一困难的环节，提出一种简单的确定可行方向的方法．该方法几何意义明确，计算快捷，容易理解，克服了解非线性约束优化问题时，Zoutendijk可行方向法有时会失效的问题。     

电磁连铸中梯约束效应的数值模拟

在连续铸刚中,控制钢的初期凝固有减小波纹状的表面振痕,对生产无表面缺陷的铸坯是极端重要的。由磁流体力学理论可知,利用交变磁场地磁约束效应,实现弯月与结晶器壁之间的“软接触”,从而能生产无表面缺陷的铸坯,在电磁连铸中,确定弯月面形状是磁约束计算中的重要内容,也是成功实现电磁连铸的关键,以基于高频高磁场的方形冷坩埚电磁连铸（４Ｃ过程）作为研究对象,导出以感应电流作为未知量的描述弯月面形状的流体和电磁等     

约束位置的修改对振动模态的影响

结构的约束位置对其固有振动特性有重要的影响，因此计算固有振动特性对约束位置的敏度是结构优化以及模型校正等的重要基础性工作．本文从广义变分原理出发，建立了约束位置的小修改导致的固有值和振动模态增量的方程，针对模态增量方程的求解，提出了一种处理原本征函数空间不完备的方法，从而可以在扩展的原本征函数空间内对振型增量进行展开．针对模态截断问题，本文又提出了一种“模态展开＋幂级数民开”的混合展开法，这种展开法的收敛性好，收敛程度易于估计，实用方便．     

DYNAMIC INTERACTION OF PLANE WAVES WITH A UNILATERALLY FRICTIONALLY CONSTRAINED INCLUSION-TIME DOMAIN BOUNDARY ELEMENT ANALYSIS

A 2D time domain boundary element method (BEM) is developed to solve the transient scattering of plane waves by a unilaterally frictionally constrained inclusion. Coulomb friction is assumed along the contact interface. The incident wave is assumed strong enough so that localized slip and separation take place along the interface. The present problem is in effect a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip, separation and stick regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embeddedin an infinite solid.     

论Vacco模型与Chetaev模型之间的关系

本文在深入研究非完整约束的几何性质和力学性质的基础上：（１）应用经典的Ｈａｍｉｌｔｏｎ原理推导出Ｖａｃｃｏ方程；（２）在Ｖａｃｃｏ方程的基础上，应用判定理想约束的力学原理，推导出Ｃｈｅｔａｅｖ条件，实现了从Ｖａｃｃｏ模型向Ｃｈｅｔａｅｖ模型的过渡；（３）论证了Ｖａｃｃｏ模型与Ｃｈｅｔａｅｖ模型是相辅相成的，从而统一了这两种模型。     

METHOD BASED ON DUAL-QUADRATIC PROGRAMMING FOR FRAME STRUCTURAL OPTIMIZATION WITH LARGE SCALE

The optimality criteria (OC) method and mathematical programming (MP) were combined to found the sectional optimization model of frame structures. Different methods were adopted to deal with the different constraints. The stress constraints as local constraints were approached by zero-order approximation and transformed into movable sectional lower limits with the full stress criterion. The displacement constraints as global constraints were transformed into explicit expressions with the unit virtual load method. Thus an approximate explicit model for the sectional optimization of frame structures was built with stress and displacement constraints. To improve the resolution efficiency, the dual-quadratic programming was adopted to transform the original optimization model into a dual problem according to the dual theory and solved iteratively in its dual space. A method called approximate scaling step was adopted to reduce computations and smooth the iterative process. Negative constraints were deleted to reduce the size of the optimization model. With MSC/Nastran software as structural solver and MSC/Patran software as developing platform, the sectional optimization software of frame structures was accomplished, considering stress and displacement constraints. The examples show that the efficiency and accuracy are improved.     

蜂窝锥壳卫星适配器约束阻尼层振动抑制分析

主要研究在蜂窝锥壳卫星适配器上附加约束阻尼来抑制锥壳传递振动。尽管约束阻尼方面的研究很多，但是大多数都是针对简单的梁或者板结构，而对复杂蜂窝锥壳结构的振动抑制问题研究还很少；为此，通过对蜂窝壳的等效化处理和约束阻尼结构的有限元建模理论分析，建立起卫星一适配器结构在有无附加约束阻尼情况下的有限元模型，进一步通过模态分析和频响分析，得到不同约束阻尼层设计参数对结构振动抑制影响规律。分析结果对于经济有效的设计约束阻尼层和结构减振减重具有较好的参考价值。     

Dynamic and buckling analysis of a thin elastic-plastic square plate in a uniform temperature field

The nonlinear models of the elastic and elasticlinear strain-hardening square plates with four immovably simply-supported edges are established by employing Hamilton‘s Variational Principle in a uniform temperature field. The unilateral equilibrium equations satisfied by the plastically buckled equilibria are also established. Dynamics and stability of the elastic and plastic plates are investigated analytically and the buckled equilibria are investigated by employing Galerkin-Ritz‘s method. The vibration frequencies, the first critical temperature differences of instability or buckling, the elastically buckled equilibria and the extremes depending on the final loading temperature difference of the plastically buckled equillibria of the plate are obtained. The results indicate that the critical buckling value of the plastic plate is lower than its critical instability value and the critical value of its buckled equilibria turning back to the trivial equilibrium are higher than the value. However, three critical values of the elastic plate are equal. The unidirectional snap-through may occur both at the stress-strain boundary of elasticity and plasticity and at the initial stage of unloading of the plastic plate.     

圆形截面约束阻尼梁整体有限元建模与振动分析

为克服约束阻尼结构在工程应用中存在的由三维有限元建模造成的单元数目巨大的问题,本文提出了圆形实心截面梁附加约束阻尼层横向振动的整体有限元建模方法,并基于此模型,研究了材料的物理属性和几何因子对这类结构的固有频率的影响。通过与三维有限元解法相比较,证明了该方法的可行性与正确性,并给出了该方法的适用范围。     

三维约束下幂硬化双材料界面裂尖场分析

本文用Ｊ２形变理论分析了三轴应力约束下，由具有不同硬化指数和硬化系数的幂硬化材料构成的界面裂纹问题．通过在本构方程中引入三轴应力约束因子Ｔｚ，我们考虑了三维约束效应对裂尖场的影响．计算结果表明，三轴应力约束对裂尖场的分布，尤其是对径向应力σｒ和有效应力σｅ有重要影响．本文还探讨了三轴约束和材料性能对裂尖应力奇异性的影响