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Which equation correctly describes Hamilton’s principle used in FEM?

(a) 0=\(\int_{t_1}^{t_2}\)[δK-(δU+δV)]dt

(b) 0=\(\int_{t_1}^{t_2}\)t[δK-(δU+δV)]dt

(c) 0=\(\int_{t_1}^{t_2}\)[δK+(δU+δV)]dt

(d) 0=\(\int_{t_1}^{t_2}\)t[-δK+(δU+δV)]dt

This question was posed to me in examination.

My query is from Shear Deformable Plate Model topic in portion Bending of Elastic Plates of Finite Element Method

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The correct answer is (a) 0=\(\int_{t_1}^{t_2}\)[δK-(δU+δV)]dt

Explanation: Governing equations of displacement-based plate theories are derived using the principle of virtual displacements. The principle of virtual displacements or Hamilton’s principle requires that 0=\(\int_{t_1}^{t_2}\)[δK-(δU+δV)]dt where δU, δV and δK denote the virtual strain energy, virtual work done by externally applied forces, and virtual kinetic energy, respectively. These quantities are expressed in terms of actual stresses and virtual strains, which depend on the assumed displacement functions and their variations.

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