Analysis of large deformations of membrane shells by the generalized finite difference method.

*(English)*Zbl 0624.73101An application of the finite difference method on arbitrary irregular grids (generalized FDM) to the numerical analysis of large deformations of membrane shells is considered.

A description of the deformation of shells was chosen that is optimal for numerical analysis by means of the FDM (it can also be effectively applied in the FEM). In this formulation deformations are referred to a reference configuration, with initial or current positions of particles assumed as independent variables. The formulation permits easy changes of constitutive law (mostly nonlinear) as well as changes of the type of problem considered (e.g. a search for the initial configuration of a membrane shell). A generalized FDM in the local formulation has been applied [T. Liszka and J. Orkisz, ibid. 11, 83-95 (1980; Zbl 0427.73077)]. The fully automatic package of computer programs FIDAMF [J. Cendrowicz, T. Liszka and the author, Proc. V. Conf. Comput. Methds. Struct. Mech. Vroclav, Poland, Vol. 2, 29-36 (1981)], was used, starting from mesh generation, including generation and solution of nonlinear FD equations up to graphic presentation of the final results.

Capabilities of the method were demonstrated by means of numerical analysis of a variety of problems of large deformations of membrane shells. Some test problems oriented toward analysis of accuracy and convergence of results were solved, as well as a variety of more complex examples (membranes of various shapes, pneumatic store, pneumatic dam and problems with unknown initial configuration).

A description of the deformation of shells was chosen that is optimal for numerical analysis by means of the FDM (it can also be effectively applied in the FEM). In this formulation deformations are referred to a reference configuration, with initial or current positions of particles assumed as independent variables. The formulation permits easy changes of constitutive law (mostly nonlinear) as well as changes of the type of problem considered (e.g. a search for the initial configuration of a membrane shell). A generalized FDM in the local formulation has been applied [T. Liszka and J. Orkisz, ibid. 11, 83-95 (1980; Zbl 0427.73077)]. The fully automatic package of computer programs FIDAMF [J. Cendrowicz, T. Liszka and the author, Proc. V. Conf. Comput. Methds. Struct. Mech. Vroclav, Poland, Vol. 2, 29-36 (1981)], was used, starting from mesh generation, including generation and solution of nonlinear FD equations up to graphic presentation of the final results.

Capabilities of the method were demonstrated by means of numerical analysis of a variety of problems of large deformations of membrane shells. Some test problems oriented toward analysis of accuracy and convergence of results were solved, as well as a variety of more complex examples (membranes of various shapes, pneumatic store, pneumatic dam and problems with unknown initial configuration).