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Stiffness Matrix Using Direct Method-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: Spring, Stiffnessk, Characteristic, Matrix, Force, Displacement, Equations, Direct, Method, Coefficient
This assignment solution was submitted to Amar Sharma for Finite Element Method course at Aligarh Muslim University. It includes: Spring, Stiffnessk, Characteristic, Matrix, Force, Displacement, Equations, Direct, Method, Coefficient
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Assignment SCIENCES Q.No.5.22. Consider a spring with stiffness k as shown in Figure 5.12. Determine the stiffness matrix of the spring using the direct method. Solution: The force-displacement equations of a step constitute the required element equations. To derive these equations for a typical element we isolate the element as shown in Figure. In this figure, force (F) and displacement (q) are defined at each of the two nodes in the positive direction of the x axis. The element equations can be expressed in matrix form as Or Where [k] is called the stiffness or characteristic matrix, u is the vector of nodal displacements, and P is the vector of nodal forces of the element. We shall derive the element stiffness matrix from the basic definition of the stiffness coefficient, and for this no assumed interpolation polynomials are needed. In structural mechanics, the stiffness influence coefficient kij is defined as the force needed at node i (in the direction of x) to produce a unit ..

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