基于增强的物质点法的非均质弹性材料仿真方法研究

在基于物理的仿真领域,近几年流行的物质点法已经成为一种越来越重要的仿真方法.物质点法已经可以仿真雪、物质状态变化、颗粒状的沙子以及粘弹性的泡沫等物理现象.现有的各种复杂物理现象的模拟已经展示了物质点法作为一种通用的求解方法的潜质,然而对于仿真形变体尤其是自然界普遍存在的非均质材质还存在一些不足.当同一网格内部包含多种材质的粒子时,由于背景网格与粒子之间的插值只考虑粒子的几何位置而不包含物质属性信息,导致不同属性的粒子在网格内部表现为"平均化"的运动趋势.为了改进传统物质点法模拟多种材质的缺陷,该文提出了一种模拟非均质弹性材料的仿真方法.首先,在预处理过程中将仿真物体离散表示成粒子,针对物质的不同属性粒子的分布,建立物质边界并确定边界粒子,仿真过程中动态更新边界粒子的位置;其次,引入粒子影响域,区分网格内部具有不同属性的粒子,增加网格内部计算自由度;最后,提出一个判断准则,根据物质边界粒子的位置判定仿真粒子是在背景计算网格上求解还是粒子区域上求解.实验结果表明,利用改进的物质点法能够有效地模拟非均质材质弹性体的形变.与有限元法相比,该文方法在模拟非均质弹性体时可以获得相似的效果,并且在模拟拓扑结构变化的问题以及碰撞处理上更有优势.

Free vibration analysis of non-homogeneous orthotropic plates resting on Pasternak elastic foundation by Rayleigh-Ritz method

Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.