美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）notes121

美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）notes122

What, in your opinion is the value of ritz's method? 1. Some. It is fraught with difficult make it almost impossible to apply to the challenging problems of design of moder aerospace structures

What new element is Castigliano s Theorem introducing? 1. None, it's just a particular case of the PMPE 2. It's a totally different principle that allows to obtain solutions of elasticity problems with unprecedented accuracy and efficiency in- cluding relativistic effects

Concept Question Which of the following statements is true 1. The PVD and the PMPE are equivalent 2. The PVD is more general 3. The PMPE applies to any kind of material 4. The stationary character of the potential en ergy is equivalent to the Pvd for elastic ma terials

Principle of Virtual Displacements Consider a body in equilibrium. We know that the stress field must satisfy the differential equations of equilibrium. Multiply the differential equations of equilibrium by an \arbitrary\displacement field T

Unit #9 -Calculus of Variations Let u be the actual configuration of a structure or mechanical system. u satisfies the displacement boundary conditions: u=u* on Su. Define

Concept Question Which of the following statements is correct? Uo=U for ALL elastic materials(1 Uo=OijEij-U0 ONLY for linear elastic materials Jo=-ijEii for a nonlinear elastic material Statements(1) and 3)

Which of the following statements is correct? 1. The PVD only applies to linear elastic materials 2. The PVD applies only to elastic materials, but they can be linear or non-linear 3. The PVD applies regardless of the constitutive behavior of the material

Unit #10- Principle of minimum potential energy and Castigliano's First Theorem Principle of minimum potential energy The principle of virtual displacements applies regardless of the constitutive law. Restrict attention to elastic materials(possibly nonlinear). Start from the Pvd