Systems Involving Unilateral Constraints

Abstract

A unilateral constraint is an idealized model of a structural component that limits some linear or angular distance to values either no greater than, or no less than, a certain magnitude. Unlike bilateral constraints, unilateral constraints are binding in only one sense of direction. Some structural components modeled as unilateral constraints in tension are wires, cables, flexible bands, membranes, fabrics, and rectilinear pin-bar chains. Situations giving rise to unilateral constraints in compression include contact problems, stacks of building blocks, springs with collapsed coils, components made of brittle, low-tensile strength materials with no reinforcement, and all kinds of liquid and granular media. Typical examples of angular, or bending, unilateral constraints are a door hinge, a spherical hinge with restraints, and a concrete beam with only a bottom reinforcement. The three most common types of unilateral constraints are shown schematically in Fig. 1.