Beschreibung
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.
Inhaltsverzeichnis
InhaltsangabeTheory.- 1 Foundation of the wave finite element method.- 1.1 Direct mathemetical modeling of wave propagation in an elastic rod.- 1.1.1 Background equations.- 1.1.2 Numerical examples.- 1.2 Wave approach to finite element modeling.- 1.2.1 Background equations of the wave finite element method (WFEM).- 1.2.2 Numerical examples.- 2 Simulation of simple one-dimensional wave processes.- 2.1 Longitudinal waves in a rod.- 2.1.1 Collision of rods of different sizes and mechanical parameters.- 2.1.2 Sudden stopping of a rod of a variable cross section.- 2.1.3 Wave propagation in a rod with inner elastic-inertial links.- 2.2 Torsional waves in a rod.- 2.2.1 Sudden stopping of a rotating shaft.- 2.2.2 Setting a disk in motion by sudden connection with a rotating shaft.- 2.3 Transverse waves in strings and cables.- 2.3.1 Waves in a string stretched by a constant force.- 2.3.2 Waves in a cable stretched by its own weight.- 3 Wave propagation in an inelastic rod.- 3.1 Longitudinal waves propagation in an inelastic rod.- 3.1.1 Discrete-continual model of an inelastic rod.- 3.1.2 Governing equations.- 3.2 Waves in a viscoelastic rod.- 3.2.1 Background equations.- 3.2.2 Numerical examples.- 3.3 Waves in an elastic-viscoplastic rod.- 3.3.1 Elastic-plastic models.- 3.3.2 An elastic-viscoplastic model.- 4 Coupled longitudinal-torsional waves in a pre-twisted rod.- 4.1 Basic equations.- 4.1.1 Governing equations for a pre-twisted rod.- 4.1.2 Wave model of a pre-twisted rod.- 4.2 Wave propagation induced by a force and torque.- 4.2.1 Waves induced by a constant load.- 4.2.2 Impulse-induced waves.- 5 Bending waves in a beam.- 5.1 Basic equations.- 5.1.1 Wave model of the Timoshenko beam.- 5.1.2 Finite element simulation of bending waves.- 5.2 Direct mathematical modeling of bending waves propagation.- 5.2.1 Structural bending/shear model of a beam.- 5.2.2 Solution procedure.- 5.3 Numerical examples.- 5.3.1 A stepped force affecting a beam.- 5.3.2 A stepped moment affecting a beam.- 5.3.3 Comparison of the DMM and WFEM approaches for bending waves modeling.- 6 One-dimensional waves in elastic continua and structures.- 6.1 Plane waves.- 6.1.1 Longitudinal waves.- 6.1.2 Transverse and coupled waves.- 6.2 Spherical and cylindrical waves.- 6.2.1 Spherical waves.- 6.2.2 Explosion in a spherical cavity of an elastic medium.- 6.2.3 Cylindrical waves.- 7 Numerical simulation of multi-dimensional wave processes.- 7.1 Foundation of the general WFEM approach.- 7.1.1 Governing equations.- 7.1.2 Waves in a plane region. Code WPRD.- 7 2 Numerical examnles.- 7.2.1 Sudden longitudinal loading of a one-side fixed plate.- 7.2.2 Sudden in-plane bending of a deep plate.- 7.2.3 A plate longitudinally impacted by a heavy body.- 7.2.4 A wide plate subjected to a bending moment.- 7.2.5 Additional remarks.- Applications.- 8 Impact loading of a deformable body.- 8.1 Principle of floating boundary conditions (FBC).- 8.1.1 Application of the FBC principle to WFEM.- 8.1.2 Special cases of body impact interaction.- 8.2 An elastic rod impacted by a rigid body.- 8.2.1 A rod of a constant cross section.- 8.2.2 The DMM accuracy in application to impact problems.- 8.2.3 A rod of variable cross section.- 8.3 An inelastic rod impacted by a rigid body.- 8.3.1 A rod of viscoelastic material.- 8.3.2 A rod of elastic-plastic material.- 8.4 Influence of contact deformation on impact response.- 8.4.1 Basic equations.- 8.4.2 Impact loading of a valve cylindrical spring.- 8.5 A pre-twisted rod impacted by a rigid body.- 8.5.1 Impact interaction of a rigid body with a pre-twisted rod.- 8.5.2 Lengthwise and turning impacts.- 9 Unsteady forced vibration of solids.- 9.1 Wave approach to study of forced vibration.- 9.1.1 Response of an elastic rod to harmonic excitation.- 9.1.2 Response of a rod of inelastic material.- 9.1.3 Transition through resonance domains under quasi-harmonic excitation.- 9.1.4 Response under fluctuating frequency and phase.- 9.2 Unsteady forced vibration of nonlinear system
