Engineering topics

Geers, T. L.

Publications and source records attributed to Geers, T. L..

4 records

NASA NTRS1973

Convergence of finite difference transient response computations for thin shells.

Numerical studies pertaining to the limits of applicability of the finite difference method in the solution of linear transient shell response problems are performed, and a computational procedure for the use of the method is recommended. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. This is not a serious limitation in view of natural constraints imposed by the extension of Saint Venant's principle to transient response problems. It is also found that the short wavelength limitations of thin shell (Bernoulli-Euler) theory create significant convergence difficulties in computed response to certain types of transverse excitations. These difficulties may be overcome, however, through proper selection of finite difference mesh dimensions and temporal smoothing of the excitation.

Sobel, L. H.↗

NASA NTRS1972

Analysis of wave propagation in elastic cylindrical shells by the perturbation method.

Description of the perturbation method for solving propagation problems of transient, axisymmetric stress waves in elastic cylindrical shells. It is shown that the method provides remarkably accurate solutions for these problems and that it can be applied to a variety of related problems, such as the propagation of compressional waves in elastic rods.

Geers, T. L.↗

NASA NTRS1972

Analysis of the transient response of shell structures by numerical methods.

This paper examines some basic considerations underlying dynamic shell response analysis and the impact of these considerations upon the practical aspects of solution by numerical methods. Emphasis is placed on the solution of linear problems. The present states of development of the finite difference and finite element methods are reviewed, and techniques for the treatment of temporal variation are discussed. An examination is made of the frequency parameters characteristic of thin shell theory, applied excitations, and spatial mesh geometries, and the significance of these parameters with respect to computational convergence is illustrated.

Geers, T. L.↗

NASA NTRS1971

Analysis of transient, linear wave propagation in shells by the finite difference method

The applicability of the finite difference method to propagation problems in shells, and the response of a cylindrical shell with cutouts to both longitudinal and radial transient excitations are investigated. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. The short wave length limitations of thin shell theory create significant convergence difficulties may often be overcome through proper selection of finite difference mesh dimensions and temporal or spatial smoothing of the excitation. Cutouts produce moderate changes in early and intermediate time response of a cylindrical shell to axisymmetric pulse loads applied at one end. The cutouts may facilitate the undesirable late-time transfer of load-injected extensional energy into nonaxisymmetric flexural response.

Geers, T. L.↗