Virtual Distortion Method

ISBN-13: 9783540537793 / Angielski / Miękka / 1991 / 176 str.

Jan Holnicki-Szulc

Opis

Virtual distortions are incompatible deIormations imposed on structures (e. g., by nonhomogeneous heating or by local imperIections) causing a compatible state OI deIormation (initial deformations) and a selI-equilibrated state OI stress (initial stresses). The theory OI virtual distortions provides an eIIicient tool which can be used to treat many problems that diIIer Irom the physical point OI view. Thermal stresses, material deIects, residual stresses in plasticity are examples OI problems that can be analysed emploing the virtual distortions approach, where the temperature Iield, dislocations and plastic distortions (permanent plastic deIormations) are described by virtual distortions. The presented approach allows the development OI eIIicient computational methods Ior numerical analysis OI such problems. States OI compatible deIormations and selI-equi1 ibrated stresses caused by virtual distortions in homogeneous and compound (biphase) bodies are analysed in the Iirst part OI the book. The results OI these considerations are explored in the next two chapters. The Iormulation OI the approach discussed in Chapter 1 and based on continuum mechanics was presented previously in the papers 5,17] while its application to the analysis OI skeletal structures was discussed in 47].

Spis treści

1. Analysis of initial stresses and deformations caused by virtual distortions.- 1.1. Distortions in elastic body.- 1.2. Analysis of stresses and deformations caused by distortions.- 1.3. Examples of structures with distortions.- 1.4. Distortions in biphase body.- 1.5. Surface distortions.- 2. Simulation by virtual distortions.- 2.1. Simulation of geometrical and physical modifications in structures.- 2.1.1. General description of simulation concept.- 2.1.2. Material distribution modifications.- 2.1.3. Simulation of unilateral constraints on stresses.- 2.1.4. Simulation of unilateral constraints on deformations.- 2.1.5. Simulation of slackened structures.- 2.1.6. Discussion.- 2.2. Simulation of shape modifications in continuous bodies.- 2.2.1. Shape modification in elastic bodies.- 2.2.2. Optimal remodeling in 2D continuum.- 2.2.3. Generalized formulation — the Michell structure.- 2.2.4. Conclusions.- 3. Optimal control by means of imposed virtual distortions.- 3.1. Passive control of stresses (prestress).- 3.1.1. Formulation of prestress problems.- 3.1.2. Minimization of global measure of stress and deformation states.- 3.1.3. Maximization of load capacity.- 3.1.4. Examples of prestress applications.- 3.1.5. Optimal surface prestress.- 3.2. Quasi-statical active control problems.- 3.2.1. Active control of structure stresses.- 3.2.2. Examples of active control of stresses.- 3.2.3. Active control of structure deflections.- 3.3. Active damping of vibration.- 3.3.1. The concept of damping through actively controlled virtual distortions.- 3.3.2. Simulation of viscous damping.- 3.3.3. Modal strategy of damping.- 3.3.4. Four degrees of freedom example.- 3.3.5. Conclusions.- 3.4. Active strategy of avoiding resonance.- 3.4.1. Optimal strategy of avoiding resonance.- 3.4.2. Example of beam with controllable support stiffness.- 3.4.3. Free vibration of beam with elastic support.- 3.4.4. Conclusions.- References.