Author | Lowe, P. G. author |
---|---|
Title | Basic Principles of Plate Theory [electronic resource] / by P. G. Lowe |
Imprint | Dordrecht : Springer Netherlands, 1982 |
Connect to | http://dx.doi.org/10.1007/978-94-011-6384-2 |
Descript | X, 180 p. online resource |
1. Preliminaries -- 1.0 Motivation -- 1.1 Vectorsโalgebra -- 1.2 Vectorsโcalculus -- 1.3 Matrices -- 1.4 Staticsโequilibrium -- 1.5 Summation convention and index notation -- 1.6 Elements of beam theory -- 1.7 Conclusions -- 2. Statics and Kinematics of Plate Bending -- 2.0 Introduction -- 2.1 The stress resultants -- 2.2 Principal values -- 2.3 The moment circle -- 2.4 Equilibrium equationsโrectangular coordinates -- 2.5 Plate bending kinematicsโrectangular coordinates -- 2.6 Equilibrium equationsโpolar coordinatesโradial symmetry -- 2.7 Plate bending kinematicsโpolar coordinatesโradial symmetry -- 2.8 Conclusions -- 3. Elastic Plates -- 3.0 Introduction -- 3.1 Elastic theory of plate bendingโmoment/curvature relations -- 3.2 Elastic theory of plate bendingโgoverning equation -- 3.3 Circular platesโradial symmetry -- 3.4 Some simple solutions for circular plates -- 3.5 Simple solutions for problems in rectangular coordinates -- 3.6 Further separation of variable featuresโrectangular plates -- 3.7 Solution by finite differences -- 3.8 Some other aspects of plate theory -- 3.9 Stability of plates -- 3.10 Conclusions -- 4. Plastic Plates -- 4.0 Introduction -- A. Solid metal plates -- B. Reinforced concrete plates -- 5. Optimal Plates -- 5.0 Introduction -- 5.1 Problem formulation -- 5.2 Constant curvature surfaces and principal directions -- 5.3 Basic resultsโcorners -- 5.4 Some complete results -- 5.5 Moment volumes -- 5.6 Some theory -- 5.7 Conclusions -- 5.8 Exercises -- 6. Bibliography and Exercises -- 6.0 Bibliography -- 6.1 Exercises -- Appendix Geometry of Surfaces -- A.0 The need for geometry -- A.1 Geometry of a plane curveโcurvature -- A.2 Length measurement on a surfaceโfirst fundamental form -- A.3 The normal to a surface -- A.4 Normal curvatureโsecond fundamental form -- A.5 The derivatives of nโthe Weingarten equations -- A.6 Directions on a surface -- A.7 The principal curvatures -- A.8 Principal directions -- A.9 Curvature and twist along the coordinate lines -- A.10 The curvature matrix -- A.11 The curvature circle -- A.12 Continuity requirements -- A.13 Special surfaces -- A.14 Summaryโthe geometrical quantities required for the construction of a plate theory