INTERNAL CONSTRAINTS AND BIFURCATIONS IN PSEUDO-RIGID BODIES

The equilibrium problem for pseudo-rigid bodies with internal constrai nts and subject to small loads is discussed. No limitations are placed on the constraints, except for the definitional axiomatic assumptions . Equilibrium configurations are obtained as critical points for a pot ential defined on the constraint manifold, a Liapunov-Schmidt reductio n is performed and a second-order expansion of the reduced potential i s obtained. This result is similar to an expansion due to Pierce for u nconstrained bodies, but here different mathematical techniques are re quired. Through a framework which is preserved from the unconstrained theory it is shown that for loads of type 0 the number and stability o f solutions is not altered by the introduction of internal constraints . By contrast, differences arise Ir hen the body is subjected to loads of type 1.