Three-dimensional anisotropic and inhomogeneous elastic media matrix analysis for small and large displacements

Summary A matrix displacement technique for analysing three-dimensional anisotropic and inhomogeneous elastic media is given for small and large displacements. The body is idealized by an assembly of finite tetrahedra. Using the novel device of natural stresses, loads and elemental stiffness, concise expressions for stiffness of the complete system are set up. Hence small displacement solution is obtained. Extension to large displacements proceeds via an incremental technique and an additional geometrical stiffness simulating effects of change of geometry on equilibrium conditions. It is proved that geometrical stiffness of tetrahedron derives from equivalent six-bar framework. Joint presence of loads and thermal actions is included.Vollständigc Fassung, mit Ausnahme der Anwendungen, des Vortrages des Verfassers beim XI. Internationalen Kongreß für Mechanik, München, August–September 1964.