Reckoning for Element Characteristics Matrix of Space Timoshenko-Beam Based on Energy Variational Principle
To analyze and calculate the element characteristics matrices of space Timoshenko-beam, research work were carried out on the basis of energy variational principle. Displacement function for the space Timoshenko-beam were put forward, the expressions for element mass matrix, stiffness matrix and load array were deduced by energy functional extremum, and the explicit forms of element mass and stiffness matrices were integrated finally. Results show that the element mass and stiffness matrices computed by this method are consistent with those in related references. It has a good theoretical and practical value in the calculation for characteristics matrices of other elements.
W. J. Pan and Z. W. Wei, "Reckoning for Element Characteristics Matrix of Space Timoshenko-Beam Based on Energy Variational Principle", Applied Mechanics and Materials, Vols. 66-68, pp. 1356-1361, 2011