Melvin L. Baron

A finite difference variational method for bending of plates

Abstract The method of analysis for bending of plates presented in this paper combines a finite difference scheme for the plate strain components and a variational derivation of the equations of motion or equilibrium. The plate strain components are expressed in terms of discrete nodal displacements with the aid of the two dimensional Taylor expansion. Consequently, the virtual work, or the first variation of the strain energy, in an area element is found as a function of the nodal displacements. The derivation of the element forces or the element stiffness matrices and the assembly of the equations of motion or equilibrium follows closely the steps of the finite element method.

Exponentially Decaying Pressure Pulse Moving With Constant Velocity on the Surface of a Layered Elastic Material (Superseismic Layer, Subseismic Half Space)

Abstract : The response of a layered elastic half-space to a progressing exponentially decaying normal surface pressure is evaluated for a case in which the constant velocity V of the moving pressure is greater than that of the P and S waves, respectively, in the upper layer (superseismic) and smaller than these wave speeds in the underlying half-space (subseismic). It is assumed that a steady-state exists with respect to coordinate axis attached to the moving load. The superseismic-subseismic geometry results in a stress field that extends over the entire plane, with sharp shocks possible only in that portion of the layer that lies behind the front of the progressing normal loading. A computer program for evaluating stresses and velocities at points in the medium is available and results are presented for a typical configuration of interest. (Author)

Pressures in a submerged fluid-filled cylindrical shell subjected to a step wave

Abstract The response of a submerged, fluid-filled, infinitely long, cylindrical shell (plane-strain ring) subjected to a step shock wave is studied to determine the effect of shell parameters (moduli, thickness, radius) on the shape of the pressure pulse transmitted inside the shell. The results show that the shell is transparent if thin enough, but, as the thickness increases, strong shell vibrations become important and distort the pulse.

Dynamic Deformation of Materials and Structures Under Explosive Loadings

Computerized analysis of materials and structures under explosive loadings has lead to the development of finite difference and finite element codes which are capable of treating nonlinear materials with a variety of dissipative mechanisms, such as thermal energy dependence, and hysteretic behavior in load-unload cycles in both shear and dilatation. Incremental plasticity theory is widely used for this purpose and a significant factor in this choice is the accompanying uniqueness — stability theory. The object of this paper is to review and illustrate this methodology for modeling nonlinear hysteretic materials and for analyzing the behavior under shock loadings of nonlinear media and structures embedded in such media.

Buckling of Vessels Composed of Combinations of Cylindrical and Spherical Shells

Abstract : The overall buckling of unstiffened cylindrical shells with hemispherical end caps is studied. Numerical results for the buckling load parameter are obtained in terms of the parameters h/a, L/a and n. The theoretical results are compared with a series of experimental results; excellent agreement between theory and experiment is noted. (Author)