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

The reaction on the left end is not exact because 1. The order of interpolation is too low, a higher order of interpolation would give the right reaction 2. The distributed load attributed to node one does not ke it into the solution

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

cmaulenon o isoparametRic elemets (Bathes book Consider the uadriltersd denat shown in the 8oc nodd coordinates

Concept Question How many quadrature points do you need to integrate exactly the stiffness matrix of a lD finite element with quadratic interpolation for the displacements? gauss

properties of finite dement soltions Noded point equilibrio At a node, the sow of he elemeat nodal forces s in equilibriun with Hhe externed loads