Description

Name of File :- Truss Analysis with FEM Design Excel Sheet

Finite Element Example – Truss Analysis

A truss problem shown in the figure above is analyzed. This problem is from figure A2.22 in Bruhn’s text book. Rod element is used and the element properties and material property are assumed as follows.

Cross Section Area: 1 inch^2

Young’s Modulus: 10 Msi

Note: This Excel file can be modified to solve any 2D problem using the following elements:

Rod with 2 end points, “ROD”
Triangular element with 3 grid points, “TRIA3”
Quadrilateral element with 4 grid points, “QUAD4”
Spring elements, “SPRING”

1. Purpose

• This spreadsheet analyzes 2-dimensional linear elastic problems using Principle of Minimum Potential Energy.

2. Modeling

• Modeling concept is same as finite element analysis.
• The element types available in this spreadsheet are Rod element, Triangular element, Quadrilateral element, and Spring element.

3. Limitation

• Number of Grids: 110 If you modify the spreadsheet, this limitation will be eliminated.
• Number of Elements: No limitation
• Material Property: Orthotropic Materials
• Element Types: Rod with 2 end points, “ROD”
• Triangular element with 3 grid points, “TRIA3”
• Quadrilateral element with 4 grid points, “QUAD4”
• Spring elements, “SPRING”

4. Instruction
4.1 Modeling

• Modeling method is same as common finite element analysis.

(1) Grid Data

• Define grid points.
• Input grid point coordinates (global coordinate system) in worksheet “grid data”.

(2) Element Data

• Input following data for each element in worksheets “ROD”,”TRIA3″, “QUAD4” and “SPRING”.
• Switch for element type usage: If you don’t use some of the element types, input “off” in column H1 .
• Grid points: Sequence of gird points in each element for “TRIA33” or “QUAD4” should be counterclockwise
• Element properties: Input cross section area for “ROD” and thickness for “TRIA3” and “QUAD4”.
• For “SPRING” element, input effective degree of freedom direction, x-direction = 1, y-direction = 2.
• Material properties: Input following data
• “ROD”: Young’s modulus
• “TRAI3” and “QUAD4”: E1, E2, v12, and G12 for principal axis
• Direction of material principal axis in global coordinate system
• For isotropic material, E1 = E2, G12 = 0.5*E1/(1+v12)
• “SPRING”: Spring constant, K
• Add rows with copying an existing row, if necessary.

(3) Constraint

• Input “1” in “Constraint” columns (H and I) of worksheet “grid data”, if the degree of freedom is constrained.
• Put zeros “0” in “Displacement” columns in worksheet “grid data”.
• Fill pink color to the “Displacement” columns with constraint.

(4) External Forces

• Input external force data in “External Forces” columns (J and K) of worksheet “grid data”.

4.2 Performing Analysis

• Prepare “Solver”. You need to add-in “Solver”.
• Select “Solver” in “Tool” function in worksheet “grid data”.
• Set parameter columns for optimization in “Solver” setup. The columns are filled in pink color in Section 4.1 (3).
• Execute “Solver”.

Calculation Reference
Bruhn