薄板弯曲运动的最小转换能量原理

本文通过Laplace变换导出了考虑转动惯量效应时各向异性的线弹性薄板在经典理论中的最小转换能量原理。文中用Laplace变换的象函数和原函数分别给出了静力学在薄板经典理论中虚功原理、最小势能原理和最小余能原理在动力学中的推广形式,并证明了前者是后者的特例。     

关于变圆形截面悬臂直梁在经典理论中的广义变分原理

考虑一个均匀的、各向同性的左端(广义)固支、右端自由的变圆形截面悬臂直梁在其铅垂的一个主平面--(x,z)平面内的弯曲问题。设x轴是梁横截面的中心线,B_1和B_2分 ...     

The general variational principle of the cantilever beam of circular cross section including transverse shear deformation

In this paper we derive the approximate theory on the straight cantilever beam of a same circular cross section including transverse shear deformation, using the general variational principle with two class variates, and we present the expression with two class variates containing two general displacement, of general complementary energy, corresponding with the theory.     

关于板的动力学的最小转换能量原理和最小值原理

本文首先通过Laplace变换导出了关于具有三个广义位移并考虑转动惯量效应时各向异性的线弹性板在动力学中的转换虚功原理和三个最小转换能量原理及其在原空间时间域中用原函数表示的对应形式,然后通过引进相容权函数的集合推导出关于空间时间域的三个最小值原理.在上述两组最小值原理中各有两个均为板在静力学中最小势能原理和最小余能原理的推广形式;而另一个最小值原理,在静力学中便没有对应形式.     

关于均匀变形的应变主方向

本文通过对非奇异线性变换的定向分解，证明了处于均匀变形的物体中，任意平面内至少存在两个互相正交的应变主方向，以及该物体内应变能密度，在上述线性变换的任意一个准主基下，可表示为５个实数的函数。     

PRINCIPLES OF MINIMUM TRANSFORMED ENERGY AND MINIMUM PRINCIPLES FOR DYNAMICS OF PLATES

In the present paper,we first by Laplace transform present a derivation of principle oftransformed virtual work, three principles of minimum transformed energy with influenceof rotatory enertia for dynamics of anisotropic linear elastic plates with three generalizeddisplacements.Moreover,the forms with the original in place-time domain correspondingthese variational principles are presented.Then by the introduction of the set of abmissible weight functions the three minimumprinciples for the original place-time domain are derivedIn each of the preceding groups of the variational principles there are two which are thedynamic counterparts to the static principles of minimum potetial energy and minimumcomplementary energy;the other principles are formulated in terms of the internal forcealone,but have no counterpart in elastostatics of plates.     

关于线性去耦热弹性动力学的最小值原理

本文推导了关于在线性去耦热弹性动力学中初-边值问题的三个具有Laplace变换的转换最小值原理和在原空间-时间域中三个加权最小值原理。     

THF GENERAL VARIATIONAL PRINCIPLE OF THE CANTILEVER BEAM OF CIRCULAR CROSS SECTION INCLUDING TRANSYERSE SHEAR DEFORIIATION

In this paper we derive the approximate theory On the straight cantilever beam of a same circular cross section including transverse shear deformation, using the general variational principle with two class variates, and we present the expression with two class variates containing two general displacement, of general complementary energy, corresponding with the theory.     

关于厚梁高阶理论非协调杂交元的矩阵方程及其解的算式

本文用二类变量广义变分原理以及应力和位移关于梁的厚度坐标的勒让德多项式的级数形式,推导了适用于厚梁高阶理论非协调杂交元的矩阵方程及其解的算式。     

关于线性粘弹性动力学的最小值原理

本文推导了在线性粘弹性动力学中三个最小值原理和关于Laplace变换的三个转换最小值原理.