Developments in Theoretical and Applied Mechanics : Proceedings of the Third Southeastern Conference on Theoretical and Applied Mechanics.
- 1st ed.
- 1 online resource (809 pages)
Front Cover -- Developments in theoretical and Applied Mechanics -- Copyright Page -- Table of Contents -- Foreword -- Preface -- Part 1.Continuum Mechanics -- Chapter 1. TIME AND DISPLACEMENT BOUND THEOREMS FOR VISCOUS AND RIGID-VISCO-PLASTIC CONTINUA SUBJECTED TO IMPULSIVE LOADING -- ABSTRACT -- NOTATION -- 1. INTRODUCTION -- 2. STABLE VISCOUS MATERIALS -- 3. MINIMUM PRINCIPLE FOR VISCOUS CONTINUA -- 4. APPLICATION TO DYNAMIC LOADING -- 5. SIMPLE VISCOUS MATERIAL -- 6. RIGID-VISCO-PLASTIC MATERIALS -- 7. CONCLUSIONS -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 2. SOME UNIQUENESS AND EXTREMUM PRINCIPLES FOR RATE-TYPE MATERIALS -- ABSTRACT -- 1. NOTATION -- 2. INTRODUCTION -- 3. A VARIATIONAL PRINCIPLE -- 4. A UNIQUENESS THEOREM FOR QUASI-STATIC DEFORMATIONS -- 5. A MINIMUM PRINCIPLE FOR QUASI-STATIC DEFORMATIONS -- 6. APPLICATION TO LINEAR MEDIA -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 3. APPROACH TO INELASTICITY THROUGH DISLOCATIONS AND EXTENDED SLAB ANALOGY -- ABSTRACT -- NOTATION -- INTRODUCTION -- SLAB ANALOGY -- SLAB ENERGY ANALOGY -- RESISTANCE OF DISLOCATION MOTION THROUGH VACANCY CLUSTERS -- CRACK INITIATION AROUND A DISLOCATION -- SLAB PLASTICITY ANALOGY -- APPENDIX I -- APPENDIX II -- APPENDIX III -- CONCLUSION -- REFERENCES -- Chapter 4. EXTENDED THEOREMS OF LIMIT ANALYSIS OF ANISOTROPIC SOLIDS -- ABSTRACT -- NOTATION -- INTRODUCTION -- VARIATIONAL PRINCIPLES -- UPPER BOUND THEOREM -- APPLICATION OF THEOREMS -- DISCUSSION AND CONCLUSION -- ACKNOWLEDGMENT -- REFERENCES -- Part 2.Elasticity -- Chapter 5. CRACK PROBLEMS IN THE THEORY OF ELASTICITY -- 1. INTRODUCTION -- 2. PHYSICAL CONSIDERATIONS -- 3. THE GRIFFITH CRACK -- 4. THE PENNY-SHAPED CRACK -- 5. THE INCLUSION OF COHESIVE FORCES -- 6. EXTERNAL CRACKS -- 7. TWO-DIMENSIONAL PROBLEMS WITH MORE COMPLICATED GEOMETRY -- 8. PENNY-SHAPED CRACKS IN CYLINDERS AND THICK PLATES. 9. DYNAMICAL PROBLEMS -- REFERENCES -- Chapter 6. FURTHER RESULTS ON CENTER OF DILATATION AND RESIDUAL STRESSES IN JOINED ELASTIC HALF-SPACES -- ABSTRACT -- NOTATION -- INTRODUCTION -- SMOOTH INTERFACE -- PERFECT BOND -- APPLICATION TO A SPHERICAL INCLUSION -- FORCE ON THE CENTER OF DILATATION -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 7. THREE-DIMENSIONAL THERMOELASTIC PROBLEMS OF PLANES OF DISCONTINUITIES OR CRACKS IN SOLIDS -- ABSTRACT -- NOTATION -- INTRODUCTION -- FUNDAMENTAL EQUATIONS OF THERMOELASTICITY -- THERMOELASTIC PROBLEMS WITH PLANES OF DISCONTINUITIES -- THE ELLIPTICAL CRACK PROBLEM -- CRACK-BORDER THERMAL STRESSES AND STRESS-INTENSITY FACTORS -- REMARKS ON A CLASS OF BOUNDARY PROBLEMS -- CONCLUSION -- APPENDIX -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 8. PLANE ELASTOSTATIC ANALYSIS OF AN INFINITE PLATE WITH A DOUBLY PERIODIC ARRAY OF HOLES OR RIGID INCLUSIONS -- ABSTRACT -- INTRODUCTION -- COMPLEX VARIABLE FORMULATION -- EQUIVALENT ELASTIC PLATE PROPERTIES -- NUMERICAL RESULTS -- CLOSURE -- ACKNOWLEDGMENT -- REFERENCES -- Part 3.Plates and shells -- Chapter 9.ON THE NONLINEAR THEORY OF THIN PLATES -- ABSTRACT -- 1. INTRODUCTION -- 2. ANALYSIS OF STRAIN -- 3. STRESS-STRAIN RELATIONS -- 4. EQUILIBRIUM EQUATIONS -- 5. DIRECT AND BENDING STRAINS IN TERMS OF DISPLACEMENT COMPONENTS -- 6. ORDER OF MAGNITUDE RELATIONS -- 7. A CALCULUS-OF-VARIATIONS CONSIDERATION -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 10. VIBRATION AND BUCKLING OF THERMALLY STRESSED PLATES OF TRAPEZOIDAL PLANFORM -- ABSTRACT -- NOTATION -- INTRODUCTION -- PLATE GEOMETRY -- THE ENERGY EXPRESSION -- THE SMALL DEFLECTION SOLUTION -- THE STRESS DISTRIBUTION -- THE DEFLECTION FUNCTION -- THE LARGE DEFLECTION SOLUTION -- THE ENERGY EXPRESSION -- SUMMARY OF RESULTS AND CONCLUSIONS -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 11. AXISYMMETRIC VIBRATION OF HEMISPHERICAL SHELLS. ABSTRACT -- NOTATION -- INTRODUCTION -- BASIC ELASTO-KINETIC EQUATIONS -- CONSTRUCTION OF THE GENERALIZED GREEN'S FUNCTIONS -- FREE VIBRATIONS OF HINGED AND COMPLETELY CLAMPED SHELL -- CONCLUSIONS -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 12. PLASTIC BUCKLING OF FLAT, SIMPLY SUPPORTED, RECTANGULAR SANDWICH PANELS OF ORTHOTROPIC CORE WITH DIFFERENT FACE THICKNESSES -- ABSTRACT -- NOTATION -- INTRODUCTION -- GENERAL PLASTICITY THEORY -- ASSUMPTIONS -- APPLICATION TO PANEL FACES -- DIFFERENTIAL EQUATIONS FROM THE MINIMUM POTENTIAL ENERGY PRINCIPLE FOR UNIAXIAL UNIFORM STRESS -- SOLUTION OF THE EQUATIONS FOR SIMPLY SUPPORTED EDGES -- SUMMARY -- ACKNOWLEDGMENTS -- REFERENCES -- CHAPTER 13.LIMIT ANALYSIS OF A CLAMPED SPHERICAL CAP USING LINEAR PROGRAMMING -- ABSTRACT -- NOTATION -- INTRODUCTION -- LIMIT ANALYSIS OF A SPHERICAL CAP -- LOWER BOUNDS USING LINEAR PROGRAMMING -- NUMERICAL RESULTS -- CONCLUSIONS -- ACKNOWLEDGMENT -- REFERENCES -- CHAPTER 14.THE DEFORMATION OF THIN SHELLS -- ABSTRACT -- NOTATION -- INTRODUCTION -- EQUATIONS OF GAUSS AND CODAZZI -- COMPATIBILITY CONDITIONS -- DISPLACEMENT -- ACKNOWLEDGMENT -- REFERENCES -- Chapter15. AN EXACT FORMULATION OF THE LINEAR EQUATION FOR THICK, ORTHOTROPIC SHELLS WITH ARBITRARY, IMPOSED TEMPERATURE AND FORCE FIELDS AND TEMPERATURE-DEPENDENT PARAMETERS -- ABSTRACT -- INTRODUCTION -- DEFINING RELATIONS -- THE THICK SHELL EQUATION HIERARCHY -- APPLICATION TO INVESTIGATION OF THIN SHELLTHEORY ACCURACY -- APPLICATION TO MULTILAYERED SHELLS -- REFERENCES -- Chapter16. MEMBRANE THEORY FOR A HEMISPHERICAL DOME SUBJECTED TO A WIND LOAD -- ABSTRACT -- NOTATION -- INTRODUCTION -- STRESS RESULTANTS -- DISPLACEMENTS -- CONCLUDING REMARKS -- ACKNOWLEDGMENT -- REFERENCES -- Part 4.Applied Mechanics -- Chapter 17. A NUMERICAL METHOD FOR THE CONFORMAL MAPPING OF FINITE DOUBLY CONNECTED REGIONS -- ABSTRACT -- NOTATION. INTRODUCTION -- DERIVATION OF THE INTEGRAL EQUATION -- SOLUTION OF THE INTEGRAL EQUATION -- CALCULATION OF THE RADIUS RATIO AND COEFFICIENTS IN THE LAURENT SERIES -- NUMERICAL RESULTS -- CONCLUSIONS -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 18. DETERMINATION OF ELASTIC COMPLIANCES OF CYLINDRICALLY AEOLOTROPIC PLATES -- ABSTRACT -- NOTATION -- INTRODUCTION -- GOVERNING EQUATIONS AND METHOD OF ANALYSIS -- DISCUSSION AND CONCLUSIONS -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 19. EXPERIMENTS ON LARGE AMPLITUDE PARAMETRIC VIBRATION OF RECTANGULAR PLATES -- ABSTRACT -- NOTATION -- INTRODUCTION -- SUMMARY OF ANALYSIS -- EXPERIMENTATION -- ACKNOWLEDGMENT -- REFERENCES -- BIBLIOGRAPHY -- Part 5.Experimental Mechanics -- Chapter 20. STRESS WAVE PROPAGATION IN A HALF PLANE DUE TO A TRANSIENT POINT LOAD -- ABSTRACT -- NOTATION -- INTRODUCTION -- THEORETICAL CONSIDERATIONS -- EXPERIMENTAL PROCEDURE -- RESULTS -- ACKNOWLEDGMENTS -- REFERENCES -- Chapter 21. THEORETICAL AND EXPERIMENTAL ANALYSES OF CREEP OF STATICALLY INDETERMINATE PORTAL FRAMES -- ABSTRACT -- NOTATION -- INTRODUCTION -- THEORY -- CORRECTED LINEAR THEORY -- EXPERIMENTAL VERIFICATION -- CONCLUSIONS -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 22. OBJECTIVE EXPERIMENTAL STRESS ANALYSIS USING THE MOIRÉ METHOD -- ABSTRACT -- NOTATION -- PRELIMINARY CONSIDERATION -- INTRODUCTION -- THEORY OF THE SYSTEM -- THE TEST -- CONCLUSIONS AND RECOMMENDATIONS -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 23. AN EXPERIMENTAL METHOD TO ANALYZE GRAVITATIONAL STRESSES IN TWO-DIMENSIONAL PROBLEMS -- ABSTRACT -- NOTATION -- INTRODUCTION -- MODEL MANUFACTURING -- METHODS OF ANALYSIS -- MODELS ANALYZED -- THE DISK UNDER ITS OWN WEIGHT -- THE RING UNDER ITS OWN WEIGHT -- THE STAR UNDER ITS OWN WEIGHT -- CONCLUSIONS -- ACKNOWLEDGMENTS -- REFERENCES -- Part 6.Wave Propagation. Chapter 24.THE PROPAGATION AND REFLECTION OF ELASTIC WAVES IN ANISOTROPIC HOLLOW SPHERES AND CYLINDERS -- ABSTRACT -- NOTATION -- INTRODUCTION -- HOLLOW SPHERE -- HOLLOW CYLINDER -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 25.DYNAMIC RESPONSE OF AN INFINITE CYLINDER TO ASYMMETRIC PRESSURE ON ITS LATERAL SURFACE -- ABSTRACT -- NOTATION -- INTRODUCTION -- DIFFERENTIAL EQUATIONS AND SOLUTIONS -- BOUNDARY CONDITIONS AND FREQUENCY EQUATIONS -- THE COMPLETE SOLUTIONS -- THE INITIAL CONDITIONS -- ILLUSTRATIVE EXAMPLE -- THE INITIAL CONDITIONS -- ILLUSTRATIVE EXAMPLE -- CONCLUDING REMARKS -- REFERENCES -- Chapter 26. STRESS WAVE PROPAGATION IN A FINITE VISCOELASTIC THIN ROD WITH A CONSTITUTIVE LAW OF THE HEREDITARY TYPE -- ABSTRACT -- NOTATION -- 1. INTRODUCTION -- 2. REVIEW OF AN ANALYTICAL SOLUTION TO A SEMI-INFINITE ROD -- 3. AN ANALYTICAL SOLUTION FOR A ROD OF FINITE LENGTH -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 27. INITIAL SHEAR STRESSES IN THE VISCOELASTIC HALF-PLANE -- ABSTRACT -- NOTATION -- INTRODUCTION -- FORMULATION -- SOLUTION -- FRONTAL SOLUTIONS -- CONCLUSIONS -- ACKNOWLEDGMENT -- REFERENCES -- Part 7.Dynamics -- Chapter 28. FIRST-ORDER SECULAR PERTURBATIONS OF AN ARTIFICIAL EARTH SATELLITE DUE TO THE SUN AND MOON -- ABSTRACT -- NOTATION -- I. INTRODUCTION -- II. THE PERTURBING FUNCTION Π -- III. LAGRANGE PERTURBATION EQUATIONS -- IV. SECULAR PERTURBATIONS OF A 24-HOUR ORBIT CAUSED BY THE SUN AND MOON -- V. CONCLUSIONS -- ACKNOWLEDGMENT -- REFERENCES -- Chapter 29. DYNAMICS OF AN ANNULAR DISK ROLLING ON ITS INNER RIM ON A CIRCULAR CYLINDER -- ABSTRACT -- NOTATION -- INTRODUCTION -- CONFIGURATION -- DYNAMICS -- APPLICATION -- ACKNOWLEDGMENT -- REFERENCE -- Chapter 30. KINEMATICS OF A THREE-AXIS GIMBAL SYSTEM -- ABSTRACT -- NOTATION -- INTRODUCTION -- CHARACTERISTICS OF A GIMBAL SYSTEM -- DERIVATION OF EQUATIONS OF CONSTRAINT. COMPUTATION OF EULER ANGULAR DISPLACEMENTS, VELOCITIES AND ACCELERATIONS.