不安定トラスの剛体変位と安定化条件

抄録

The structural problem in the unstable condition of structures like membrane structures and link structures belongs to the geometrically nonlinear problem, and primary characteristics of such an unstable structure are (1) in the existence of rigid body displacements without strain and (2) in the introduction of prestressing to change unstable into stable by giving initial stiffness. In order to understand the characteristics mentioned above, the following items are clarified in the paper by means of rigid truss models : (a) Existence condition of rigid body displaceemnts, (b) Classification of rigid body displacements into linear rigid body displacement and finite rigid body displacement, (c) Existence condition of self-equilibrated stress systems to know the possibility of introduction of prestressing, and (d) Relation between rigid body displacements and self-equilibrated stress systems of unstable structures. Since coefficient matrices of kinematic equations as well as of equilibrium equations are in general rectangular matrices, the generalized inverse is used for making the inverse relation of coefficient matrices.