THE GENERALIZED VARIATIONAL PRINCIPLES ABOUT BLENDING ENERGY FORM OF NON-LINEAR ELASTICITY

First of all,this paper gives Legendre transformation for the so-called partialcorresponding variables of strain energy function ∑(E_(ij)) and complementary strainenergy function ∑~c(S_(ij))of the elastic material,and introduces the correspondingblending complementary strain energy function ∑~c_(kl) and blending strain energy function∑_(kl).Moreover,a series of generalized variational principles of the corresponding blendingenergy form of non-linear elasticity is given.As a special case,there exist correspondingresults in linear elasticity.     

The generalized variational principles about blending energy form of non-linear elasticity

First of all, this paper gives Legendre transformation for the so-called partial corresponding variables of strain energy function Σ(E_ij) and complementary strain energy function Σc(S_ij) of the elastic materiel, and introduces the corresponding blending complementary strain energy function Σch_k! and blending strain energy function Σh_k!. Moreover, a series of generalized variational principles of the corresponding blending energy form of non-linear elasticity is given. As a special case, there exist corresponding results[1] in linear elasticity.     

非线性弹性理论的混合能量形式广义变分原理

本文首先对弹性材料的应变能函数∑(E_ij)和余应能函数∑C(S_ij)的部分“对应”变量作Legendre变换,引进“对应”的混合余应变能函数∑_klC和混合应变能函数∑_kl。进而,给出非线性弹性理论的各种“对应”的混合能量形式广义变分原理。线性弹性理论也有相应结果,它是本文结果的特殊情况。     

边界曲线坐标系

力学中许多问题要计算边界量及其边界量之间关系表达式,用以表述边界条件。例如平面应力问题的σ_(nn),σ_(ns),u_n,u_s,e_(ss),γ_(ns),λ_s,板壳理论的N_n,N_(ns),M_(nn),M_(ns),u_n,u_s等。有的教本和专著是用坐标变换的方法计算边界诸量之间的关系式,其想法是简单的,但算起来却 ...