1. write down all relevant quantities, as specifically as possible for this case: displacement functions, strain...

  

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1. write down all relevant quantities, as specifically as possible for this case: displacement functions, strain components, stress components, moments 2. express sectional forces and mom its as functions of displacement 3. derive plate equation as a differential equation and boundary conditions 4. demonstrate that total potential energy in the plate is expressed as: 2 d²u = = [ {P [~ (1²) ² - dr2 V TD • +2v duz d²uz +- dr dr² r dr 1/du ) ²] -2p(r)ru.} dr M Ø2R p(r) axisymmetric case circular plate radius R constant thickness t isotropic material E, v axisymmetric load case p(r) entire perimeter is simply supported question: derive the plate equation in a cylinder frame 1. write down all relevant quantities, as specifically as possible for this case: displacement functions, strain components, stress components, moments 2. express sectional forces and mom its as functions of displacement 3. derive plate equation as a differential equation and boundary conditions 4. demonstrate that total potential energy in the plate is expressed as: 2 d²u = = [ {P [~ (1²) ² - dr2 V TD • +2v duz d²uz +- dr dr² r dr 1/du ) ²] -2p(r)ru.} dr M Ø2R p(r) axisymmetric case circular plate radius R constant thickness t isotropic material E, v axisymmetric load case p(r) entire perimeter is simply supported question: derive the plate equation in a cylinder frame

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1 Relevant Quantities Displacement Functions Lets denote the displacements as ur r 0 and ue r 0 wher... View the full answer