Structural optimization

, Volume 9, Issue 2, pp 96–104 | Cite as

Prebuckling optimal design of orthotropic variable thickness plates for inplane loading

  • R. Levy
  • V. Sokolinsky
Technical Papers

Abstract

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.

Keywords

Sine Optimal Design Compressive Loading Variable Thickness Rectangular Plate 

Notation

A

matrix of generalized eigenvalue problem

a

vector of buckled shape amplitudes

a

plate dimension inx-direction

amn

amplitude of buckled shape of plate

B

matrix of generalized eigenvalue problem

B1B16

coefficients of cube of plate thickness

B1B9

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

D1,Dx,Dy,Dxy

flexural rigidities for orthotropic plate

\(\bar D_1 ,\bar D_x ,\bar D_y ,\bar D_{xy}\)

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

Fc

total potential for double-cosine shape representation

Fs

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

tavr

average thickness of nonuniform plate

t(x, y)

thickness varying withx andy

t1,t2,t3

shape coefficients

I1I16

types of integrals

J1J16

types of integrals

K1K5

numerical factors

L1L9

types of integrals

L(t)

differential operator

M1M9

types of integrals

m

number of waves inx-direction

MAIN

module of the FORTRAN program

Nxy

shearing force per unit distance in middle surface of plate

NWRK

parameter of the FORTRAN program

n

number of waves iny-direction

Nx

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

α

constant of proportionality

β

combination of integers

γ

numerical factor

δ

variation

ζ

numerical factor

θ

strain energy density

ν

Poisson's ratio

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References

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • R. Levy
    • 1
  • V. Sokolinsky
    • 2
  1. 1.Dept. of Civil and Environmental EngineeringPolytechnic UniversityBrooklynUSA
  2. 2.Dept. of Civil EngineeringTechnion-Israel Institute of TechnologyTechnion CityIsrael

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