Virtual Distortion Method

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.