《THE BENDING AND STRETCHING OF PLATES》求取 ⇩

PART ⅠSMALL-DEFLEXION THEORY1

Chapter Ⅰ．Derivation of the basic equations3

1．1Stress-strain relations4

1．2 Rotation of axes of reference7

1．3 Equilibrium10

1．4 Differential equation for the deflexion11

1．5 Effect of forces in the plane of the plate11

1．6 General boundary conditions16

Chapter Ⅱ．Rectangular plates21

2．1Plates with all edges simply supported21

2．2 Plates with two opposite edges simply supported25

2．3 Plates with all edges clamped31

Chapter Ⅲ．Plates of varios shapes35

3．1Circular plates35

3．2 Uniformly loaded sector plate43

3．3 Sector and wedgs-shaped plates with general boundary conditions44

3．4 Elliptical plate45

3．5 Equilateral triangular plate45

3．6 Isosceles right-angled triangular plate45

Chapter Ⅳ．Plates whose boundaries are amenable to conformal trans-formation47

4．1Governing differential equation in complex coordinatcs48

4．2 General solution for a clamped plate55

4．3 General solution for a simply supported plate58

4．4 Square plate with rounded corners59

Chapter Ⅴ．Plates with variable rigidity64

5．1Flexure and torsion of a strip of variable rigidity64

5．2 Rectangular plate with exponential variation of rigidity68

5．3 Rectangular plate with linear variation of rigidity71

5．4 Circular plates73

5．5 Circular plates with rotational symmetry76

Chapter Ⅵ．Approximate methods79

6．1The strain energy of a deformed plate79

6．2 Principle of minimum total potential energy—Ritz method82

6．3 The Galerkin method86

6．4 A variational method89

6．5 Method of boundary error minimization93

PART ⅡLARGE-DEFLEXTIN THEORY97

Chapter Ⅶ．General equations and some exact solutions99

7．1Governing differential equations99

7．2 Cylindrical deflexion of long strip100

7．3 Uniformly loaded circular plate104

7．4 Flexure and torsion of a thin strip with lateral thickness variation106

Chapter Ⅷ．Approximate methods in large-deflezion analysis114

8．1perturbation method for normally loaded plates114

8．2 Perturbation method in post-buckling problems117

8．3 An energy method122

Chapter Ⅸ．Asymptotic large-deflexion theories for very thin plates128

9．1Membrane theory128

9．2 Inextensional theory133

Author Index145

Subject Index147