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Stiffness and Mass Matrices of Bar-Finite Element Method-Assignment Solution

Exercises, Finite Element Method

Post: July 8th, 2012
Description
This assignment solution was submitted to Amar Sharma for Finite Element Method course at Aligarh Muslim University. It includes: Tapered, Bar, Length, Cross-sectional, Area, Strain, Kinetic, Energy, Matrix, Axial, Displacement
This assignment solution was submitted to Amar Sharma for Finite Element Method course at Aligarh Muslim University. It includes: Tapered, Bar, Length, Cross-sectional, Area, Strain, Kinetic, Energy, Matrix, Axial, Displacement
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Contents
Assignment#02 Finite Element Methods Statement: 1.9 For the tapered bar shown in Figure 1.20. The area of cross section changes along the length as . where A0 is the cross-sectional area at x=0, and is the length of the bar. By expressing the strain and kinetic energies of the bar in matrix forms, identify the stiffness and mass matrices of a typical element. Assume a linear model for the axial displacement of the bar element. Figure: docsity.com Solution: Step 1: Idealization As shown in the above figure the bar is distributed into three equal and same elements.  We take a typical element of length (e) with nodal unknowns 1  and  2  at nodes 1 e e and 2.we take linear displacement model of bar element.   x   1   2 x.......... 1 Step 2: At x=0 B.C’s    x   1e And at x=   x   2e Putting these conditions in equation.1 and finding them values of constants  e gives 1  1 ..

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