Plastic Analysis of Plates and Shells

Part II Plastic Analysis of Plates and Shells Professor Tomasz Wierzbicki Contents 1 Fundamentals 2 1.1 Plastic Incompressibility ............................................ 2 1.2 Yield Condition ................................................. 2 1.3 Associated Flow Rule ............................................. 4 2 Yield Conditions in the Space of Generalized Stresses 5 2.1 Pure Bending Action, N αβ =0 or n αβ =0 .................................. 7 2.2 Pure Membrane Action, M αβ =0 or m αβ =0 ................................ 7 2.3 Cylindrical Shell ................................................ 8 3 Principle of Virtual Velocity and Limit Analysis 8 3.1 Lower Bound Theorem ............................................. 9 3.2 Upper Bound Theorem ............................................. 9 4 Applications 10 4.1 Bending of a Simply Supported Plate ..................................... 10 4.2 Concept of a Plastic Hinge, and Example of a Clamped Plate . . . . . . . . . . . . . . . . . . . . . . . 13 4.3 Plastic Resistance of a Circular Membrane .................................. 15 4.4 Axial Crushing of a Prismatic Tube ..................................... 18 1

Plastic Analysis of Plates and Shells

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