Elasticity 0:10 The Energy principles and the Variational Calculus
1 Elasticity
弹单生力 第十章分活
2
Chapter 10 The Energy Principles and the variational calculus 8 10-1 The Specific Energy of Deformation and Strain Energy 0 of Elastic body 8 10-2 The Variational Equation of Displacement and The Principle of minimum Potential Energy 8 10-3 The Variational Method of Displacement 810-4 The Variational Equations of Stress and the Variational Method of stress
3 §10-1 The Specific Energy of Deformation and Strain Energy of Elastic Body §10-3 The Variational Method of Displacement §10-4 The Variational Equations of Stress and the Variational Method of Stress §10-2 The Variational Equation of Displacement and The Principle of Minimum Potential Energy Chapter 10 The Energy Principles and theVariational Calculus
熊量原与分法 第十章能量原理与变分法 §10-1弹性体的变形比能与形变势能 >§10-2位移变分方程与极小势能原理 §10-3位移变分法 p」§10-4应力变分方程与应力变分方法
4 第十章 能量原理与变分法 §10-1 弹性体的变形比能与形变势能 §10-3 位移变分法 §10-4 应力变分方程与应力变分方法 §10-2 位移变分方程与极小势能原理
The problems of the elastic theory need a series of partial differential equations. It always meet with difficulties in math. So we have to seek for approximate solution. The approximate solution of variational calculus is a method in common use. In math, variational problems are the problems to solve the limit of the functional. In elastic mechanics. the functional is the energy( work) of elasticity problems. And the variational calculus is to s calculate the extremum of the energy ( work). We can yield the solution of the elastic problems when calculating the extremum. The direct method of variation problems facilitate us to obtain the approximate solution We will give the expressions which calculate the potential energy of strain at first in this chapter. We will mainly introduce the variational method of displacement and that of stress through the relation of work and energy
5 The problems of the elastic theory need a series of partial differential equations. It always meet with difficulties in math. So we have to seek for approximate solution. The approximate solution of variational calculus is a method in common use. In math, variational problems are the problems to solve the limit of the functional. In elastic mechanics, the functional is the energy(work) of elasticity problems. And the variational calculus is to calculate the extremum of the energy(work). We can yield the solution of the elastic problems when calculating the extremum. The direct method of variation problemsfacilitate us to obtain the approximate solution. We will give the expressions which calculate the potential energy of strain at first in this chapter. We will mainly introduce the variational method of displacement and that of stress through the relation of work and energy