The Wave Finite Element Method

Computational mechanics, as a science employed for the numerical model ing of processes in nature and engineering, has over the last few decades developed two strands. The first concerns the putting of more and more powerful software packages into computational practice, using increas ingly high-performance computers with increasingly large memory. The traditional finite element and finite difference approaches are still preva lent. Over the years however, researchers have met with new problems; their solutions on the basis of traditional methods are at best difficult and at worst impossible to obtain. Such problems provided a powerful impetus in the development of the second strand, resulting in the development of es sentially new approaches for numerical modeling, for example meshless methods, "molecular" dynamics, neuron networks. The current state of the art formed the basis of many papers presented at the Fifth World Congress on Computational Mechanics, Vienna 2002. It is within the framework of the second strand that this book has been written.

A new more efficient and accurate Finite Element Method for structural analysis is presented in this scientific monograph Includes supplementary material: sn.pub/extras

Klappentext

This monograph presents in detail the novel "wave" approach to finite element modeling of transient processes in solids. Strong discontinuities of stress, deformation, and velocity wave fronts as well as a finite magnitude of wave propagation speed over elements are considered. These phenomena, such as explosions, shocks, and seismic waves, involve problems with a time scale near the wave propagation time. Software packages for 1D and 2D problems yield significantly better results than classical FEA, so some FORTRAN programs with the necessary comments are given in the appendix. The book is written for researchers, lecturers, and advanced students interested in problems of numerical modeling of non-stationary dynamic processes in deformable bodies and continua, and also for engineers and researchers involved designing machines and structures, in which shock, vibro-impact, and other unsteady dynamics and waves processes play a significant role.

Zusammenfassung
Computational mechanics, as a science employed for the numerical model­ ing of processes in nature and engineering, has over the last few decades developed two strands. The first concerns the putting of more and more powerful software packages into computational practice, using increas­ ingly high-performance computers with increasingly large memory. The traditional finite element and finite difference approaches are still preva­ lent. Over the years however, researchers have met with new problems; their solutions on the basis of traditional methods are at best difficult and at worst impossible to obtain. Such problems provided a powerful impetus in the development of the second strand, resulting in the development of es­ sentially new approaches for numerical modeling, for example meshless methods, "molecular" dynamics, neuron networks. The current state of the art formed the basis of many papers presented at the Fifth World Congress on Computational Mechanics, Vienna 2002. It is within the framework of the second strand that this book has been written.

Inhalt
Theory.- 1 Foundation of the wave finite element method.- 2 Simulation of simple one-dimensional wave processes.- 3 Wave propagation in an inelastic rod.- 4 Coupled longitudinal-torsional waves in a pre-twisted rod.- 5 Bending waves in a beam.- 6 One-dimensional waves in elastic continua and structures.- 7 Numerical simulation of multi-dimensional wave processes.- Applications.- 8 Impact loading of a deformable body.- 9 Unsteady forced vibration of solids.- 10 Unsteady vibro-impact loading.- 11 Oscillations of a mechanical system affected by moving loads.- 12 Dynamic loading of a free edge of a solid.- 13 Some special problems of solid mechanics.- 14 Some special unsteady problems in engineering.- Conclusion.- References.