1 LINEAR & NONLINEAR PLATE THEORY Contents Strain-displacement relations for nonlinear plate theory (pg. 2) Stress quantities, Principle of Virtual Work and equilibrium equations (pg. 4) Linear elastic constitutive relation for plates (pg. 7) von Karman nonlinear plate equations (pg. 9) Solutions to several linear plate problems (pg. 10) Circular plates with clamped and simply supported conditions A rectangular plate subject to concentrated loads at its corners A simply supported rectangular plate subject to a general pressure distribution A rectangular plate clamped on two edges and simply supported on the other two Solutions to nonlinear plate problems—coupled bending and stretching (pg. 17) Two examples of plate vibrations (pg. 23) Examples of classical plate buckling problems (pg. 26) Homework Problem #7: Stationarity of potential energy of the plate system (pg.8) Homework Problem #8: Minimum PE for linear bending theory of plates (pg. 8) Homework Problem #9: Axisymmetric deformations of circular plates (pg. 10) Homework Problem #10: Rectangular plate with concentrated corner forces (pg.11) Homework Problem#11: An approximate solution for a square clamped plate subject to uniform pressure (pg. 17) Homework Problem #12: Nonlinear membrane solution for a beam with zero bending Stiffness (pg. 20) Homework Problem #13: Vibration frequencies and modes of a simply supported rectangular plate (pg. 24) Homework Problem #14: Variational principle for buckling eigenvalue problem (pg. 29) Homework Problem #15: Buckling of an infinitely long clamped plate ( pg. 31) Homework Problem #16: Buckling of a rectangular plate with one free edge ( pg. 32)
LINEAR & NONLINEAR PLATE THEORY
Jun 19, 2023
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