Reference no: EM13869219
Question 1: Concepts of Solid Mechanics
Objective: Apply basic concepts of solid mechanics, e.g. displacement field, strain and stress tensors. The displacement ???? in a second-order (quadratic) element is calculated from the FEA of static analysis of a linear elastic, isotropic, homogeneous solid as following
u = 2.0 * 10-4(x1 + 2x2 - x3)e1 + 1.0 * 10-4x2x3e2 - 1.5 * 10-4(x1 - x3)2e3
(Note: the displacements and the coordinates have the same length unit, m)
At point P(4, 2, 2), determine:
- The displacement vector;
- The strain tensor;
- The stress tensor, given E = 200 GPa and ν = 0.3; and
- If the yield strength of this material is 550 MPa, is the material safe at point P according to von Mises yield criteria?
Question 2: FEA of a 1-D bar system
Objectives:
To understand bar element and know how to use it to analyse a 1-D bar system
A system consisting of three bars is shown in the following figure and all the parameters of the members are given in the figure as well.
![457_FEA of a 1-D bar system.jpg](https://secure.expertsmind.com/CMSImages/457_FEA of a 1-D bar system.jpg)
With the minimum number of linear elements, determine:
- the element stiffness matrices for each part;
- the assembled global stiffness matrices;
- the boundary conditions in the system;
- the condensed matrix equations for the unknown displacements after applying the boundary conditions;
- the displacement at each interface for two neighbouring parts;
- the reaction forces applied at the left end of the bar;
- the internal forces in each part; and
- the internal stress in each part.
Question 3: Structural Analysis of a planar truss
Objectives:
1 To understand truss element and know how to use FEA to analyse a truss structure. A planar truss structure is shown in the following figure and all the parameters of the members are given in the figure as well:
![721_Structural Analysis of a planar truss.jpg](https://secure.expertsmind.com/CMSImages/721_Structural%20Analysis%20of%20a%20planar%20truss.jpg)
Determine:
- the transformed element stiffness matrices for each truss member;
- the assembled global stiffness matrix;
- the boundary conditions at each node;
- the condensed matrix equations for the unknown displacements after applying the boundary conditions;
- the displacements at each node when the load is applied statically;
- the internal forces in each truss member; and
- the internal stress in each truss member.
Question 4: FEA of Beam Structure
Objectives:
To understand beam element and know how to use it to analyse a 1-D beam system subjected to combined loadings.
Use the minimum number of Euler-Bernoulli beam elements, which only one beam element is used for one part made of a material, to analyse the beam structure as depicted in the image below subjected to combined loading.
![1820_FEA of Beam Structure.jpg](https://secure.expertsmind.com/CMSImages/1820_FEA of Beam Structure.jpg)
(a) Determine:
- the element stiffness matrices for each part;
- the assembled global stiffness matrices;
- the boundary conditions in the system;
- the condensed matrix equations for the unknown displacements after applying boundary conditions;
- the displacement at each interface for two neighbouring parts;
- the reaction forces and moments; and
- the maximum stress in each part.
(b) Use Abaqus to run a static analysis of this problem.
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