Stability, Bifurcation and Postcritical Behaviour of Elastic Structures

摘要: 1. The Liapunov Theory of Equilibrium Stability (M. Pignataro). Differential equations. Simple types equilibrium points. points non-linear systems. according to Liapunov. Theorems on the stability equilibrium. Analysis by linear approximation. Criterion negative real parts all roots a polynomial. 2. and Post-Buckling Behaviour Discrete Mechanical Systems Lagrange Hamilton equations motion. Lagrange-Dirichlet theorem. Chetayev. discrete A system one degree freedom with: Stable symmetrical post-critical behaviour Unstable Asymmetrical Non-linear pre-critical behaviour. two degrees freedom. 3. Bifurcation for Systems. Characterisation Points an Path from Examination Local Properties (N. Rizzi). analysis properties belonging path. Perturbation method in asymptotic determination regular paths through point Q. Search critical along known path local bifurcated vicinity bifurcation point. Outlines starting approximate 4. Post-Critical Continuous instability. Critical condition continuous Construction means perturbation analysis. 5. Beams Plane Frames Rizzi, M. Beam models. load beams loaded axially at end. Particular problems. Simply supported beam mid-span. beams. Symmetric, simply supported, bar frame. Hinged portal Application finite elements problems plane frames. 6. Thin-Walled with Open Cross-Section (A. Luongo). Hypotheses mechanical thin-walled Kinematics beam. Formulation linearised problem stability. Thin-walled subjected to: Uniform compression Eccentric axial loads Under pure bending. Flexural-torsional lateral loads. Methods discretisation. Outline 7. Plates Shells Luongo, Some basic results theory surfaces shells. Elastic strain energy. plates. of: Rectangular plates Stiffened