Prebuckling optimal design of orthotropic variable thickness plates for inplane loading

This paper is concerned with the optimal design of orthotropic rectangular plates for shear and compressive buckling loads. Expressions for the total potential as series summations are derived for double cosine thickness varying plates and hybrid double sine thickness varying plates. An efficient Fortran coded program for analysis of simply supported plates that utilizes the Rayleigh-Ritz method until convergence has been developed. It incorporates an optimization module that reactivates analysis as required. Four types of orthotropic plates were optimized in a one parameter optimization search. Results indicate a 33% increase in capacity for shear loading and an 89% increase in capacity for compressive loading.Notation A matrix of generalized eigenvalue problem - a vector of buckled shape amplitudes - a plate dimension inx-direction - a _mn amplitude of buckled shape of plate - B matrix of generalized eigenvalue problem - B ₁ –B ₁₆ coefficients of cube of plate thickness - B ₁ –B ₉ coefficients of square of plate thickness - b plate dimension iny-direction - CCEF parameter of the FORTRAN program - COEF parameter of the FORTRAN program - COEFFICIENTS module of the FORTRAN program - D ₁,D _x,D _y,D _xy flexural rigidities for orthotropic plate - flexural rigidities for orthotropic plate per cubic thickness - DI1-DI16 modules of the FORTRAN program - DI1A-DI16A modules of the FORTRAN program - DIO1-DIO9 modules of the FORTRAN program - DIO1A-DIO9A modules of the FORTRAN program - E Young's modulus - EIGEN module of the FORTRAN program - F total potential energy of buckled plate - F _c total potential for double-cosine shape representation - F _s total potential for hybrid shape representation - FK1-FK16 modules of the FORTRAN program - FK1A-FK16A modules of the FORTRAN program - FKS1-FKS16 modules of the FORTRAN program - FKS1A-FKS16A modules of the FORTRAN program - t _avr average thickness of nonuniform plate - t(x, y) thickness varying withx andy - t ₁,t ₂,t ₃ shape coefficients - I ₁ –I ₁₆ types of integrals - J ₁ –J ₁₆ types of integrals - K ₁ –K ₅ numerical factors - L ₁ –L ₉ types of integrals - L(t) differential operator - M ₁ –M ₉ types of integrals - m number of waves inx-direction - MAIN module of the FORTRAN program - N _xy shearing force per unit distance in middle surface of plate - NWRK parameter of the FORTRAN program - n number of waves iny-direction - N _x normal force inx-direction in middle - OPTIMIZER surface of plate - OPTIMIZER module of the FORTRAN program - p integer - POSTMAN module of the FORTRAN program - q integer - S area of plate - T work of external forces - U strain energy of bending - V volume of plate - w lateral displacement of plate - {W} vector of derivatives (–w, _xx ; –w _yy ;w _xy ) - x coordinate direction - y coordinate direction - z coordinate direction - constant of proportionality - combination of integers - numerical factor - variation - numerical factor - strain energy density - Poisson's ratio On leave from the Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel