弹性力学状态变量体系下带有初应力的振动问题

通过在Hellinger-Reissner广义势能中引入应变的非线性项,推导出了弹性力学Hamilton体系下的具有初应力的振动方程,并运用精细积分给出了两端简支的梁、组合梁和四边简支板及组合板在初应力下振动频率。本文结果是严格弹性力学意义(没有引入任何几何变形假设)下的精确解,为衡量各种计入剪切变形的薄板、中厚板理论的准确性提供了一个标准。     

人教版高中物理新教材“问题”栏目的优化设计研究

教材是学科核心素养发展的重要课程资源.人教版高中物理新教材的“问题”栏目,有助于激发学生的学习兴趣,培养学生的问题意识.但在教学意义、素材来源、内容表述等方面还存在不足.针对这些不足,本文力图对“问题”栏目进行优化设计,使其真正能够促进学生的主动探究,促进对知识的深度理解,促进学生的物理学科核心素养的发展.     

Vibration and stability of hybrid plate based on elasticity theory

The governing equations of elasticity theory for natural vibration and buck- ling of anisotropic plate are derived from Hellinger-Reissner＇s variational principle with nonlinear strain-displacement relations. Simply supported rectangular hybrid plates are studied with a precise integration method. This method, in contrast to the traditional finite difference approximation, gives highly precise numerical results that approach the full computer precision. So the results for natural vibration and stability of hybrid plates presented in the paper can be riewed as approximate analytical solutions. Furthermore, several types of coupling effects such as coupling between bending and twisting, and coupling between extension and bending, when the layer stacking sequence is asymmetric, are considered by only one set of governing equations.     

弹性混合板的振动和稳定问题

通过将非线性应变位移关系引入Hellinger-Reissner变分原理,推导出了各向异性板基于弹性理论下的振动和屈曲控制方程.用精细积分法研究了四边简支混合矩形板.精细积分法与传统的有限差分法相比,可以给出计算机精度允许的很精确的数值结果.所以,给出的混合板的振动和稳定的结果可以看作是近似解析的.这些结果可以作为衡量各种板理论准确性的一个标准.而且,非对称层合板中出现的各种耦合影响,比如弯扭耦合,拉弯耦合等在同一组控制方程里被考虑了.