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Development of Beam Equations

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Development of Beam Equations. Potential Energy Approach to Derive Beam Element Equations. The total potential energy for a beam is. The stress/strain relationship is:. where. The total potential energy in matrix form:.

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Development of Beam Equations

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  1. Development of Beam Equations

  2. Potential Energy Approach to Derive Beam Element Equations The total potential energy for a beam is

  3. The stress/strain relationship is: where The total potential energy in matrix form: Differentiating with respect to and equating each term to zero to minimize we obtain

  4. Galerkin’s Method for Deriving Beam Element Equations The basic differential equation for beam is: Applying Galerkin’s criterion We now apply integration by parts twice to the first term:

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