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A High-Order Theory of Plate Deformation—Part 1: Homogeneous Plates
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1977
Year
EngineeringMechanical EngineeringStructural OptimizationHomogeneous PlatesStructural EngineeringMechanicsStructural DynamicDeformation ModelingMaterial NonlinearitiesPlate DeformationSolid MechanicsStructural DesignExact Elasticity SolutionMechanical DeformationThin-walled StructurePart 2Civil EngineeringStructural AnalysisStructural MechanicsMechanics Of Materials
The study focuses on homogeneous plates, with a subsequent part addressing laminated plates. The authors derive a high‑order plate deformation theory that incorporates transverse shear, transverse normal strain, and a nonlinear in‑plane displacement distribution across thickness. The theory is validated by comparing its predictions for a plate under sinusoidal surface pressure with both lower‑order plate theories and the exact elasticity solution. When the load pattern’s characteristic length is comparable to the plate thickness, lower‑order theories fail and the high‑order theory is necessary for accurate results.
A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower-order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with the exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower-order theories are inadequate and the present high-order theory is required to give meaningful results. The present work treats homogeneous plates while Part 2 involves laminated plates.