# 有限元复习资料-缩印版

1.What is the difference between the strong and weak forms of system equations?(强形式、弱形式区别)：强形式：要求强的连续性，可微次数必须等于存在于系统方程中偏微分方程的次数。弱形式：通常是积分形式，要求较弱的连续性，基于弱形式的公式通常可以得到一组更逼近于真实解的离散的系统方程。

2. What are the conditions that assumed displacement has to satisfy in order to apply the Hamilton’s principle?（应用哈密尔顿原理必须满足的条件）：协调性方程、本质边界条件、初时刻和末时刻的条件。

3.Briefly describe the standard steps involved in the finite element method.（有限元的步骤）：域的离散、位移插值、局部坐标系中有限元方程的形成、坐标转换、整体有限元方程的组装、施加位移约束、求解有限元方程。

4.Do we have to discretize the problem domain in order to apply the Hamilton’s principle? What is the purpose of dividing the problem domain into elements?（必须离散问题域吗？为什么要离散？）：不必须；为了更好地假设位移场的参数。

5. How many DOFs does a 2-nodal, planar truss element have in its local coordinate system, and in the global coordinate system? Why is there a difference in DOFs in these two coordinate systems?（两节点平面桁架单元在局部和整体坐标系中各有多少个自由度？为什么？）：在局部坐标系中有两个自由度，整体

6.What are the

characteristics of the

joints in a truss structure

and what are the effects of

this on the deformation and

stress properties in a truss

element?（桁架结构的节点特征

（2）一个桁架结构仅仅有轴向

7.Explain why the

superposition （叠加）

technique can be used to

formulate the frame elements

simply using the

formulations of the truss and

beam elements. On what

conditions this

superimposition technique

will fail. （为什么桁架+梁=

8.Explain the reasons to

cause over-stiff behavior

associate with the

displacement-based finite

element method.(位移有限元

9.Briefly comment the

of Lagrange multilier method

to implement MPC

equations(拉格朗日乘子法的

10. Briefly comment the

of penalty method to

implement MPC equations（罚

11.If the thickness

variation of a linear

rectangular element,how many

Gauss points are required to

evaluate exactly the element

mass and stiffness matrices?

h N T N，应变矩阵N是关于ξ and

η的线性函数，而厚度h是关于

n=2m-1，可知需2X2,4个高斯

11.Give at least three

applications to use

MPCequations.(举出三个多点

12.Why should the local

coordinate system be

introduced toform FE

equations?And why should the

FE equations in local

coordinatesystem also be

transformed to global

coordinate system?(为什么引

13.How to fprm a crack tip

element?(如何形成裂纹尖端单

1/4边长的距离，其他点与普通

mechanics assumptions

between thin plate and thick

plate? And what’s

differences to assume their

FEM shape function?(从弹性力

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1.The dimension of local element stiffness matrix for spatial truss is().空间桁架的局部刚度矩阵是（1X1）方阵。

2.In a 2D solid problem,if x direction displeacement of node 4 is zero,which row and column of global stiffness should be deleted to impose the constraint?在二维固体问题中，如果节点4的X方向位移为零，则在总刚矩阵中哪一行哪一列应该被删除？（7行7列）

3.The dimension of coordinate transformation matrix for planar truss is().平面桁架的坐标转换矩阵是（2X4）矩阵。

4.In a planar frame element,its local node 1 and 2 correspond its node 5 and 8.Where should the element k43 of element stiffness be located in global stiffness?(22行15列)

5.A coordinate transformation matrix belongs to (orthogonal) matrix.坐标转换矩阵是(正交矩阵)

triangular element,the shape

function N4 indicated by area

coordinate is(4L1L2)在六节

7.Equation described the

relationship between the

stress and strain is called

（Constitutive equation）描

displacement components in a

tetrahedron(四面体)element

are (12)四面体单元节点位移

9.The number of each nodal

displacement components in a

rectangular shell element

with 4 nodes are(6)在4节点

10.In any element,(any

points in the element satisfy

shape function)满足形函数的

1.When an element stiffness

matrix is partitioned into

sub-matrices according to

nodes,the subscripts of each

sub-matrices are(局部)nodal

number.可将单元刚度矩阵ke

2.After assembling the

global stiffness,the nodal

displacement vector can’t

be solved although the nobal

reason is the global

stiffness is a(奇

（奇异性）的，为此必须（施加

3.Whenglobal stiffness

matrix is partitioned into

according to nodes,the

subscripts of each

sub-matrices are identified

as(总体)nodal number。总刚矩

displacement used in

Hamilton’s principle must

satify 3 conditions,they

are(协调性方程、本质边界条

5.Three sufficient

requirements for FEM shape

functions are(德尔塔函数性

6.The two same properties for

both element stiffness and

global stiffness are(对称性、

8.Four type structural

symmetries can be used to

simplify modelling

process,which are (镜面对称、

9.When the weighted residual

approach is used to formulate

the FEM system equations and

the shape functions are used

to as the weight function,the

method is called as(迦辽金法)

10.There are 5 type element

distortions, which are(长宽

（）

11.二维固体中，宽度为16，最

12.节点总数为10，带宽为15

13.5节点4个单元组成的平面

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