光测弹性理论中耦联系统的变分原理
The Variational Principles of Coupled Systems in Photoelasticity
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摘要: 本文提出一能量原理,即光测弹性理论中耦联系统的零差功原理,并据此原理导出了光测弹性理论中耦联系统的势能、余能,广义势能和广义余能变分原理。所谓耦联系统是指形状、尺寸、载荷和边界条件全同且都处于真实状态但材料不同的两个变形体。光测弹性理论中的原型体和模型体实质上是耦联系统,因而上述原理就成为确定柏松比v对冻结应力法精度影响的理论基础。Abstract: This paper presents an energy principle,zero different principle of coupled systems in photoelasticity,from which potential energy,complementary energy,generalized potential energy and generalized complementary energy variational principles of the coupled systems in photoelasticity are derived. What is called the coupled systems means that two deformational bodies,forwhich figures,sizes,loads and boundary conditions are the same and they are all inactual states but they are made of different materials.Prototype body and model body in photoelasticity are essentially the coupled systems,therefore the above principles become the theoretical basis of defining the influnce of Poissons ratio v on accuracy of the frozen-stress method.
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[1] 钱伟长、叶开沅,《弹性力学》,科学出版社,北京(1956). [2] 钱伟长,《广义变分原理》,知识出版社,北京(1985). [3] Kyuirhire Washizu,Variational Methods in Elasticity and Pfasticity,Pergamon Press
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