有限位移理论线弹性力学二类和三类混合变量的变分原理及其应用

发布时间：2018-04-03 22:18

本文选题：有限位移理论　切入点：线弹性力学　出处：《应用数学和力学》2017年11期

【摘要】：提出了有限位移理论线弹性力学二类混合变量和三类混合变量的变分原理.考虑已知边界条件的变化并应用有限位移理论的功的互等定理,在导出上述两类变分原理的过程中起到了关键作用和桥梁作用.首先,考虑已知位移边界条件的变化和应用功的互等定理,导出了二类混合变量的最小势能原理.用类似的方法,导出了二类混合变量的驻值余能原理.应用应变能密度和应力余能密度的关系式于上述两个变分原理,得到三类混合变量的变分原理.然后,给出了二类和三类混合变量的虚功原理和虚余功原理.同时,应用拉氏乘子法导出了广义变分原理.以一个算例说明了在某些情况下拉氏乘子法会失效,介绍了构成广义变分原理泛函的半逆法.最后,应用二类混合变量最小势能原理计算了一大挠度悬臂梁的弯曲.
[Abstract]:The finite displacement theory of elastic mechanics of two mixed variables and three kinds of mixed variational principle. Considering the variation of the known boundary conditions and the reciprocal theorem is applied to the finite displacement theory of power, in deriving the above two kinds of variable process principle plays a key role in bridge and role. First of all, mutual theorem and application of power change considering the known displacement boundary conditions, the principle of minimum potential energy is derived two kinds of mixed variables. Using similar methods, stationary complementary energy principle derived two kinds of mixed variables. Based on the strain energy density and stress energy density relationship for the above two variational principle three, class of mixed variational principle. Then, the principle of virtual work principle and virtual work are two and three kinds of mixed variables. At the same time, the application of Lagrange multiplier method derives a generalized variational principle. An example is given to illustrate in some situations The Lagrangian multiplier method will fail. The semi inverse method is introduced to form the functional of generalized variational principle. Finally, the bending of a large deflection cantilever beam is calculated by using the minimum potential energy principle of the two kind of mixed variables.

【作者单位】：燕山大学建筑工程与力学学院;
【分类号】：O343

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