Analysis of cracks in solids 论文

摘要

Introduction: Modelling of solids with cracks - Elements of convex analysis Approximation methods Problems with singular boundaries. Cracks in plates and shells: Viscoelastic contact problem for a plate A plate under creep conditions A plate with vertical and horizontal displacements Contact problem for a plate having a crack Cracks of minimal opening in plates Solving methods for plates with cracks Contact problem for a shell with a crack Signorini problem for cracks in shells Simplified nonpenetration conditions in contact problems Solving methods for the simplified models. Cracks in complicated plates: Plate with a crack under the creep condition Contact of two plates one of which has a crack Thermoelastic plates with cracks Cracks of minimal opening in thermoelastic plates Inclined cracks in plates Friction problem for plates with cracks. Variation of cracks in solids: Variation of a crack length A plate with a crack A crack moving to the external boundary A case of a shallow shell A crack near the boundary Asymptotics of the energy functional for the Poisson equation Asymptotics of the energy functional for the Lam? equations Three-dimensional case Extreme crack shapes in a shallow shell. Cracks in elastoplastic bodies: Elastoplastic problems for the Hencky model Elastoplastic problems for the Prandtl-Reuss model Elastoplastic problems for plates with cracks The Prandtl-Reuss elastoplastic plates Contact elastoplastic problem for the curvilinear Kirchhoff rod Contact elastoplastic problem for the curvilinear Timoshenko rod Viscoelastoplastic curvilinear Timoshenko rod Curvilinear rod under creep conditions Conclusion.