MULTI-VARIABLE VARIATIONAL PRINCIPLES FORPLATE BENDING AND PLANE ELASTICITY
板弯曲与平面弹性问题的多类变量变分原理

In this paper, the multi-variable variational principles for plate bending and plane elas-ticity are presented, which included all the boundary integral formulas. The variational principlefor plate bending covers five classes of equations of equilibrium, bending moment function-bendingmoment, curvature-deflection, compatibility, bending moment-curvature and all boundary condi-tions, in which independent variables are deflection, curvature, non-homogeneous bending moment,bending moment functions and bending moment. And the one for plane elasticity covers five classesof equations of compatibility, displacement-strain, stress function-stress, equilibrium and stress-strain, in which independent variables are stress function, stress, residual strain, displacement andstrain.The multi-variable variational principles combine the Hu-Washizu as well as Pro-HW varia-tional principles into one, it is the most general variational principle so far. Not only it can beapplied to elasticity problem with residual strain, and also multi-variable variational principle forthe shallow shell can be proposed, which is based on the analogy between plate bending and planeelasticity problems.