IDENTIFICATION



User’s Information Manual for COSHELL: Computer Program for the Analysis of Discretely Stiffened Laminated Composite Cylindrical Shells

By

Samuel K. Kassegne, PhD

Internal Report

Engineering Science and Mechanics Department

Virginia Polytechnic Institute and State University

Blacksburg, VA 24061

January 1993

IDENTIFICATION

Program Name: COSHELL

(Analysis of Discretely Stiffened Laminated COmposite SHELLs)

Purpose: Linear stress, linearized buckling, natural vibration, nonlinear and post-buckling analysis of stiffened composite cylindrical shells using the Layerwise shell theory.

Programmer: Samuel K. Kassegne

Engineering Science and Mechanics Department, Virginia Polytechnic Institute and State University (VPI & SU), January 1993.

INTRODUCTION

COSHELL is a FORTRAN program developed for the analysis of laminated composite cylindrical shells stiffened by discrete stiffeners. The Layerwise shell theory is used to model the shell or plate skin. A Layerwise theory is also used for the stiffener elements. The Layerwise shell theory reduces a 3D problem to a 2D problem by expanding the 3D displacement field as a function of a 2D displacement field surface-wise and a 1D interpolation function through the thickness. Higher degrees of accuracy can be obtained by an appropriate selection of the interpolation functions. The theory, apart from accurately predicting global responses such as deflections, vibration frequencies, critical buckling loads and post-buckling paths, has a clear advantage in its ability to accurately predict local quantities like normal and transverse shear stresses and strains. The details of the Layerwise shell theory and the finite element model for discretely stiffened shells are given in Reference [3].

The program COSHELL needs geometry, material properties, stacking sequence and loading conditions as an input. The output consists of interface displacements at each nodal point, stresses and strains in both the skin and the stiffeners at nodal and Gauss points.

At the present stage, COSHELL can be used to model axially and circumferentially stiffened laminated plates and shells. There is no imposed limit on the number of stiffeners or finite elements used in the program. There is a plan to extend the capability of the program to analyze plates and shells stiffened by criss-crossing geodesic stiffeners.

DATA INPUT

1 Units

The variables used in the program are not assigned any particular system of units. However, consistency must be maintained once a particular system of units is selected.

2 Coordinate Systems

Two right-handed orthogonal Cartesian coordinate systems are used.

1) Global System (X, Y, Z)

A global system of coordinates is chosen for the whole cylindrical shell such that the x-axis lies in the direction of the span of the shell.

2) Local System (Y, Z)

The stiffeners have their own local coordinate system. The axial stiffeners (stringers) lie in the X-Z plane whereas the circumferential stiffeners (rings) lie in the Y-Z plane. Coordinates of the stiffeners are entered in the local coordinate systems.

3 Idealization of Stiffened Shells

The usual criterion of convergence of displacements, strains and stresses should be employed to choose an appropriate finite element mesh for the skin and stiffeners. There should be consistency in selecting the elements, i.e., if the user employs nine-noded quadrilateral elements for the shell or plate skin, the corresponding three-noded quadrilateral beam elements should be used for the stiffeners.

Through the thickness of the stiffeners and the skin, it is preferable to use at least two linear elements.

4 DATA ENTRY

i) Title Card (Card Set 1) – Enter 1 line of identification statements.

ii) Control Cards (Card Set 2)

(Basic model parameters are defined in this card)

NELEM - number of elements in the mesh

NPE - number of nodes per element (4 or 9)

NNODE - total number of nodes in the mesh

MAXIT - maximum number of iterations for a nonlinear analysis.

NLOAD - number of load cases

NEIGEN - 1 for eigenvalue analysis; 0 otherwise.

IPROB - 1 for buckling analysis

0 for natural vibration analysis

IPOST - 1 for post-buckling analysis; 0 otherwise

IR - 1 for full Newton-Raphson scheme

0 for modified Newton-Raphson Scheme

iii) Card Set 3

PX - uniform axial load

PW - uniform transverse surface load

EPSLON - tolerance limit for nonlinear solution

NPRT - 1 for printing stiffness and mass matrices

2 for printing mesh and nodal coordinates

0 otherwise.

NRED - 0 for full integration

1 selective reduced integration (Qi4 and Qi5 terms only).

2 selective reduced integration (Qi3 term only)

3 selective reduced integration (Qi3, Qi4, and Qi5 terms)

4 uniformly reduced integration (on all terms)

ICODE - 0 for calculating stress at the nodes

1 for calculating stress at Gauss Points

ILOD - 0 for uniform external pressure

1 for uniform internal pressure

2 for both internal and external pressure

DLAM - initial arc length (for post-buckling analysis)

ISTART - code for restart analysis

0 for no read/write option

1 for write only

2 for read only

3 for read and write option

iv) Card Set 4

IAXIAL - 1 for axial inplane load (buckling analysis)

ILATER - 1 for lateral load (buckling analysis)

IREAD - 0 for boundary conditions entered long-hand

1 for boundary conditions entered short-hand

KNOD - number of nodes where the boundary conditions are specified

ISMEAR - 0 for unstiffened shells

1 for full discrete approach

2 equivalent discrete approach

3 smeared approach

IMPFCT - 1 for imperfection sensitivity analysis

0 otherwise

ISINE - 0 for uniform load

1 single sinusoidal load (both x and y directions)

2 single sinusoidal load (x direction only)

3 single sinusoidal load (y direction only)

v) Card Set 5 – Connectivity Matrix

((NOD(N ................
................

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