Dynamic Analysis of Non-Linear Structures by the Method of Statistical Quadratization

ISBN-13: 9783540527435 / Angielski / Miękka / 1990 / 172 str.

M. G. Donley; P. D. Spanos

Opis

This text deals with a new technique for the dynamic analysis of nonlinear structures, which allows engineers to deal with complex nonlinear problems in a systematic manner. It is especially relevant in dealing with offshore structures which are exposed to nonlinear forces due to waves.

Spis treści

1: Introduction.- 1.1 Introduction.- 1.2 Aim of Study.- 1.3 TLP Model.- 1.4 Environmental Loads.- 1.4.1 Methods to Compute Viscous Forces.- 1.4.2 Methods to Compute Potential Forces.- 1.5 Literature Review of TLP Analyses.- 1.6 Scope of Study.- 2: Equivalent Stochastic Quadratization for Single-Degree-of-Freedom Systems.- 2.1 Introduction.- 2.2 Analytical Method Formulation.- 2.3 Derivation of Linear and Quadratic Transfer Functions.- 2.4 Response Probability Distribution.- 2.5 Response Spectral Density.- 2.6 Solution Procedure.- 2.7 Example of Application.- 2.8 Summary and Conclusions.- 3: Equivalent Stochastic Quadratization for Multi-Degree-of-Freedom Systems.- 3.1 Introduction.- 3.2 Analytical Method Formulation.- 3.3 Derivation of Linear and Quadratic Transfer Functions.- 3.4 Response Probability Distribution.- 3.5 Response Spectral Density.- 3.6 Solution Procedure.- 3.7 Reduced Solution Analytical Method.- 3.8 Example of Application.- 3.9 Summary and Conclusions.- 4: Potential Wave Forces on a Moored Vertical Cylinder.- 4.1 Introduction.- 4.2 Volterra Series Force Description.- 4.3 Near-Field Approach for Deriving Potential Forces.- 4.3.1 Fluid Flow Boundary Value Problem.- 4.3.2 Perturbation Expansion.- 4.4 Linear Velocity Potential.- 4.5 Added Mass Force.- 4.6 Linear Force Transfer Functions.- 4.6.1 Wave Diffraction Force.- 4.6.2 Wave Diffraction Moment.- 4.6.3 Hydrodynamic Buoyancy Force.- 4.6.4 Comparison to Morison’s Equation.- 4.7 Quadratic Force Transfer Functions.- 4.7.1 Wave Elevation Drift Force.- 4.7.2 Wave Elevation Drift Moment.- 4.7.3 Velocity Head Drift Force.- 4.7.4 Velocity Head Drift Moment.- 4.7.5 Body Motion Drift Forces and Moment.- 4.7.6 Numerical Examples for Fixed Vertical Cylinder.- 4.8 Transfer Functions for Tension Leg Platform.- 4.8.1 Modification of Cylinder Transfer Functions.- 4.8.2 Numerical Example for Tension Leg Platform.- 4.9 Summary and Conclusions.- 5: Equivalent Stochastic Quadratization for Tension Leg Platform Response to Viscous Drift Forces.- 5.1 Introduction.- 5.2 Formulation of TLP Model.- 5.3 Analytical Method Formulation.- 5.4 Derivation of Linear and Quadratic Transfer Functions.- 5.5 Response Probability Distribution.- 5.6 Response Spectral Density.- 5.7 Axial Tendon Force.- 5.8 Solution Procedure.- 5.9 Numerical Example.- 5.10 Summary and Conclusions.- 6: Stochastic Response of a Tension Leg Platform to Viscous and Potential Drift Forces.- 6.1 Introduction.- 6.2 Analytical Method Formulation.- 6.3 Numerical Results.- 6.3.1 Response to Quadratic Drag Force.- 6.3.2 Response to Quadratic Wave Elevation/Velocity Head Force.- 6.3.3 Response to Quadratic Body Motion Force.- 6.3.4 Response to Combined Viscous and Potential Quadratic Forces.- 6.3.5 Evaluation of Newman’s Approximation.- 6.3.6 High Frequency Axial Tendon Force.- 6.4 Summary and Conclusions.- 7: Summary and Conclusions.- Appendix A: Gram-Charlier Coefficients.- A.1 Introduction.- A.2 Gram-Charlier Coefficients.- Appendix B: Evaluation of Expectations.- B.1 Introduction.- B.2 Expectations Involving Quadratic Nonlinearity.- B.3 High Order Central Moments.- Appendix C: Pierson-Moskowitz Wave Spectrum.- Appendix D: Simulation Methods.- D.1 Introduction.- D.2 Linear Wave Simulation.- D.3 Linear Wave Force Simulation.- D.4 Drag Force Simulation.- D.5 Quadratic Wave Force Simulation.- References:.