Stiffness Matrix Of Beam Element Research Articles

Coupled bending–torsional dynamic stiffness matrix for beam elements

AbstractExplicit expressions for the coupled bending–torsional dynamic stiffness matrix of a uniform beam element are derived in an exact sense by solving the governing differential equation of the beam. Implementation of the derived dynamic stiffness matrix in a space frame computer program is discussed with particular reference to an established algorithm to enable vibration analysis of coupled systems to be made. The application of the theory is demonstrated by an illustrative example wherein the results for a cantilever beam with a substantial amount of coupling between bending and torsion are highlighted. The correctness of the theory is confirmed to a high degree of accuracy by computed results and numerical checks.

Curved beam element stiffness matrix formulation

Stiffness matrix of order 12 × 12, for a curved beam element has been formulated involving all the forces together, using Castigliano's theorem. Effects of transverse shear forces and tangential thrust are also taken into account. In earlier works, stiffness submatrices for the two uncoupled systems of forces are formulated independently and then they are combined to give the overall 12 × 12 matrix. A program subroutine, NEWCBM for the stiffness matrix formulation of curved beams has been written in FORTRAN which can be added to the element library of general purpose computer programs like SAP-IV and its improved versions. Example problems have been worked to check the accuracy of this formulation.

Power series expansion of the general stiffness matrix for beam elements

AbstractThe general stiffness matrix for a beam element is derived from the Bernoulli–Euler differential equation with the inclusion of axial forces. The terms of this matrix are expanded into a power series as a function of the two variables: the axial force, and; the vibrating frequency. It is shown that the first three terms of the resulting series, which are derived in the technical literature from assumed static displacement functions, correspond respectively to the elastic stiffness matrix, the consistent mass matrix, and the geometric matrix. Higher order terms up to the second order terms of the series expansion are obtained explicitly. Also a discussion is presented for establishing the region of convergence of the series expansion for the dynamic stiffness matrix, the stability matrix, and the general stiffness matrix.