Beam model refinement and reduction

In this paper we present a method for systematic construction of the stiffness matrix of an arbitrary spatial frame element by performing a series of elementary transformations. The procedure of this kind is capable of including a number of element refinements (addition of shear deformation, variable cross-section, etc.) that are not easily accessible to standard displacement-based method. We also discuss the necessary modifications of the element stiffness matrix in order to accommodate different constraints, such as point constraints in terms of joint releases (or hinges) for moments or shear forces. This is obtained by means of model reduction providing a more effective approach than the alternative one in which the global number of degrees of freedom has to be increased by one for each new release. Finally, we elaborate upon the global constraints imposing the length-invariant deformation of frame elements with an arbitrary position in space. Several numerical examples are used to illustrate the performance of the proposed procedures. The computations are carried out by a modified version of computer code CAL.