유한요소 해석 - stiffness matrix

소개

유한요소 해석의 핵심인 stiffness matrix를 트러스 구조물을 예로들어 설명한 발표자료(발표 대본 있음)

목차

Introduction of Given Truss Structure
Hand Calculation with Stiffness Method
Finite Element Method by MIDAS
Comparison
Conclusion

본문내용

Introduction of Given Truss Structure
P1=2k
P2=4k
10ft
10ft
Hand Calculation with Stiffness Matrix
Number nodes and element
tributions
Apply B.C and Calculate unknown joint displacement
Assembly
Derivation of global stiffness matrix
Make stiffness matrix
Hand Calculation with Stiffness Matrix
F = kx
Hand Calculation with Stiffness Matrix
Global stiffness matrix
ASSEMBLED !!
Hand Calculation with Stiffness Matrix
d2x=d3x=d3y= 0, f4x= 2000, f4y= -4000



You know this equation, don’t you? It’s Hooke’s law.
In the finite element method and in analysis of spring systems.
a stiffness matrix, K,
where F and x are the force and the displacement vectors
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This is global stiffness matrix.
It’s too complicated
Assemble all element stiffness matrix to global stiffness matrix.
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Input the boundary conditions as follows, then we can get these kinds of displacements at each joint.
Then from now, I’ll check this result to the FEM result came from MIDAS analysis.
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I’ll introduce the algorism of FEM program briefly.
First input the data like the no. of elements and nodes, angle of element, elastic modulus and section area etc. then, the program set K and F which is global stiffness matrix and forces matrix to zero. And other processes are totally same to processes of hand calculation so I’ll omit the explanation in here.
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These are result of comparison between hand cal, computer cal.
we tried to compare with indirect way by use of displacement factor. This column is hand calculation displacement ….
As you can see their result are some error.
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