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25 Number analysis of thin Appendix assembled system bending and shear Bending Stiffness Matrix bending-stiffness bilinear form CENTRAL DEFLECTION Combining equations components Conference on Matrix convergence criteria coordinate systems denoted discrete Kirchhoff hypothesis discrete system displacement field displacement vector displacements and rotations elastic Equations 30 finite element method finite element representation finite number FLAT PLATES function GEOMETRY OF DEFORMATION Global nodal global values high-order polynomial approximation Huntsville in-plane displacements kinematic Lagrangian strain tensor linear Melosh membrane stiffness matrix Metric tensor middle plane middle surface Mixed derivative nodal displacements nodal lines nodal points nodal quantities nondimensional nonlinear plate problems Number of Elements OL OL plate element POLYNOMIAL COEFFICIENTS potential energy rectangular Row Column Shear Stiffness Matrix shear strains simple bilinear approximation Square Plate SQUARE PLATE-CASE strain energy strain-displacement relations stresses table are defined Tangent base vector thin plates typical finite element undeformed plate Utku vector field