A direct numerical method to evaluate the geometric stability of arbitrary spatial structures

Abstract

Each structural designer has to ensure that the load-bearing structure to be designed is geometrically stable; i.e. the structure does not exhibit any spurious kinematic modes. Existing methods evaluating this requirement are either indirect and thus computationally inefficient, or restricted to 2- or 3-dimensional pin-jointed structures or to 2-dimensional general structures. In order to close this gap, a new method is proposed that is able to handle arbitrary spatial structures, consisting of arbitrarily shaped 1-, 2- and 3-dimensional bodies (e.g. truss, beam, plate, shell, solid), which are arbitrarily connected to each other in reference to their types (e.g. rigid, pin-jointed, torsional joint, shear force and bending connection) and their acting spots (at points, along a line or over a plane). The same holds for the support. The proposed method is based on a kinematic approach, where only translational degrees of freedom are considered. It has been proved that 8 different types of kinematic constraints are required to evaluate the geometric stability of a general spatial structure; all these constraints are stated explicitly. With the resulting constraint matrix, the geometric stability can be evaluated, and all existing spurious kinematic modes can be calculated. The new method can simply be added as an extra module to the existing structural analysis software.