A numerical method for static or dynamic stiffness matrix of non-uniform members resting on variable elastic foundations

This paper presents a generalized numerical method which is based on the well-known Mohr method. Static or dynamic stiffness matrices, as well as nodal load vectors for the static case, of non-uniform members are derived for several effects. The method focuses on the effects of resting on variable one- or two-parameter elastic foundations or supported by no foundation; a variable iterative algorithm is developed for computer application of the method. The algorithm enables the non-uniform member to be regarded as a sub-structure. This provides an important advantage to encompass all the variable effects in the stiffness matrix of this sub-structure. Stability and free-vibration analyses of the sub-structure can also be carried out through this method. Parametric and numerical examples are given to verify the accuracy and efficiency of the submitted method.