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Finite Element Analysis Using MATLAB

Problem #1 Structural Analysis (Truss beam frame and grid)

Objective

The aim of the first problem was to analyze the truss structure using a truss element to determine its deformation (nodal displacements) and reactions in elements when subjected to nodal loading. The analysis was carried out using MATLAB program. 

Problem Statement

The 3D truss structure will undergo finite element analysis (FEA) for two specific load cases:

  • Case 1: A force of Fy = -40,000 N is applied at nodes 13 and 14.

  • Case 2: A force of Fy = 80,000 N is applied at node 5, and a force of Fy = -40,000 N is applied at node 22.

 

There are total of 71 truss elements and 26 nodes, and total degree of freedom of 26*3=78 because each nodes has 3 global degrees of freedom. The pin constraints in all degrees of freedom at the four upper corners.

 

The material constants used in the finite element model are shown below: 

E=70GPa (Young’s modulus of Aluminum) 

A=0.1 m  (cross section area of the aluminum truss element) 

The length of each truss element is determined automatically using MATLAB code to generate the stiffness matrix. As this problem simplifies using only truss elements, each element is subject to uniform axial stress and strain throughout every cross-section."

2

MATLAB Results

(N)

(N)

Problem #2 Solid Simulation (2D or 3D) 

Objective

The aim of this problem is to design a 2D solid structure with rectangular plane elements (Bilinear rectangle,Q4) to perform finite element analysis using MATLAB program to obtain the nodal displacements, with post-processing. 

Problem Statement

There are total of 80 rectangular elements and 115 nodes, and total degree of freedom of 115*2=230 because each nodes has 2 global degrees of freedom. The pin constraints in all degrees of freedom at the base corners.

The material constants used in the finite element model are shown below: 

E= 70GPa (Young’s modulus of Aluminum)

Poisson’s ratio = 0.26

Plate thickness = 0.05 m 

Width and height of each rectangular element : 1m and 1m 

MATLAB Results

(N)

Displacement along the x-axis

Displacement along the y-axis

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