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

一、目的和要求 1、掌握车用发动机的基本工作原理与构造 2、掌握车用发动机的主要参数的检查、调 整方法和维护使用技能。 3、为后继专业课程和在今后的工作中从事 汽车发动机设计、研究、生产、修理打下基 础。 二、学习方法 认真听课,认真做实验,将书本上的理 论知识与实物结合起来学习

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