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

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

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

美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）notes121

the finite derwent meThod Ir position of boundary conditions(olis plcewent) We had obtained the aesewbed finite element eeve Kik2∞ Kht K Ki

The finite element melod I In FEM I We derived basis functions of arbitrary order for Hhe rod Model

he finite element Metnod Overcome limitations of Rita Simple basis functions( ow order polyuouisls) Basisfonctians supported in sdo domains(fuite elemnet Basis functions constructed to provide interpolant of proximate soluton Undetermined beraweters represent vales of dead

The correct global local node mapping for the quadraticelement mesh in the figure is

Finite element wodel of a beam(Euler-Bernollia- governing eQuations

Numerical integration Consider He 4-D integral =+(s 1 Seek n-point apploxiwisfions G~2M =1 are the weights and