中文摘要：

基于刚体模型的交互虚拟装配仿真已在产品可装配性验证、装配工艺规划、操作培训与指导等方面得到大量应用,但装配过程的变形仿真涉及零部件的变形和应力计算,目前仍是虚拟装配领域的问题之一。装配变形对于薄壁结构更为突出,如飞机机身、汽车车身制造领域。目前的有限元法（Finite element method,FEM）在速度上无法满足交互虚拟装配仿真需求,而常用的弹簧-质子模型也无法用于薄壁件变形计算。提出基于平面三角形网格几何模型的薄壁件弹性变形力学模型,从平面三角单元出发采用高阶Laplace变形法构建薄壁件弹性变形基本求解方程,并给出边界条件处理方法。与常规的有限元板壳模型计算结果进行了对比,结果表明所提出的薄壁件变形力学模型具有较高的求解效率,并且更容易与目前的虚拟装配仿真集成,将可用于支持薄壁结构交互装配仿真过程的变形和应力计算。

英文摘要：

Interactive assembly based on rigid body geometric model is widely used in product assimilability testing, assembling process planning and operation training. Due to the difficulties on calculating the part deformation and stress during assembling process, the deformable parts assembling simulation is still a problem in the area of virtual assembly. The deformation during assembling is more important for thin-wall structures, such as aircraft body, ship body and so on. The numerical methods as a f＇mite element method （FEM） can＇t meet the requirement of computing speed during interactive assembling simulation. Other methods based on spring-mass model can＇t be used to calculate bending effect of a thin-wall part. A mechanical model based on planar triangles gird of thin-wall part is proposed to calculate the elastic deformation. From the planar triangular element, a high-order Laplace deform method is used to construct the basic equation for elastic deformation computing. The comparison of our model and typical shell model of FEM shows that our computing model has a higher efficiency and a better integration with the interactive virtual assembly system for calculating the deformation and stress of thin-wall structures.