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Thin Plate Theory Kirchhoff Plate TheoryAssumptions similar to those in the beam theory: A straight line along the normal to the mid surface remains straight and normal to the deflected

ThS Nguyễn Thái Hiền

Email: thnguyen@hcmut.edu.vn

Phone: 0909450208

Facebook: thaihienvl@yahoo.com

5.1 Introduction

5.2 Shell modeling

5.3 Exercises

Thin Plate Theory ( Kirchhoff Plate Theory)

Assumptions (similar to those in the beam theory):

A straight line along the normal to the mid surface remains straight and normal to the deflected mid surface after loading, that is, these

is no transverse shear deformation:

0

xz yz

   

Thick Plate Theory (Mindlin Plate Theory)

If the thickness t of a plate is not “thin”, t/L = 1/10 (L = a characteristic dimension of the plate), then the thick plate theory by Mindlin should be applied This theory accounts for the angle changes within a cross section, that is,

   

Shells and Shell Elements

Shells – Thin structures witch span over curved surfaces.

Example:

Sea shell, egg shell (the wonder of the nature);

Containers, pipes, tanks;

Car bodies;

Name Element Description Notes

SHELL181 4-Node Structural Shell 6 dof at each node

SHELL281 8-Node Structural Shell 6 dof at each node SHELL163 Explicit Thin Structural Shell 12 dof at each node SHELL209 3-Node Axisymmetric Shell

SHELL208 2-Node Axisymmetric Shell

SHELL131 4-Node Thermal Shell

SHELL132 8-Node Thermal Shell

Shell elements in ANSYS

- Element Description:

SHELL181 is suitable for analyzing thin to moderately-thick shell structures It is a four-node element with six degrees of freedom at each node: translations in the x, y, and z directions, and rotations about the x, y, and z-axes (If the membrane option is used, the element has translational degrees of freedom only) The degenerate triangular option should only be used as filler elements in mesh generation.

SHELL181 is well-suited for linear, large rotation, and/or large strain nonlinear applications Change in shell thickness is accounted for in nonlinear analyses.

SHELL181 may be used for layered applications for modeling composite shells or sandwich construction.

SHELL181 Input Data

- SHELL181 Geometry

SHELL181 Input Data

- Single-Layer Definition

To define the thickness (and other information), use section definition, as follows:

- Multilayer Definition

The shell section commands allow for layered shell definition Options are available for specifying the thickness, material, orientation, and number of integration points through the thickness of the layers.

Ex1:Curved shell with a rectangular hole

Using the input data listed below the stress distribution should be calculated for a shell with a rectangular hole.

Given:

E = 210000 MPa

 = 0,3

FX = 10 kN

FZ = 1 kN

800

500

1200

500

300

t = 10

R=600

Fx

Fz

Ex1:Curved shell with a rectangular hole

/PREP7

ET,1,181

SECTYPE,SHELL

SECDATA,10

MP,EX, 1, 210000

MP,NUXY, 1, 0.3

CSYS,5

K,1,600,0,0

K,2,600,40,0

K,3,600,40,1200

K,4,600,0,1200

K,5,600,0,500

K,6,600,25,500

K,7,600,25,800

K,8,600,0,800

A,1,2,3,4

AMESH,ALL

CSYS,0

ARSYM,Z,3,,,, ! reflection Include nodes and elements

NUMM,NODE ! Merges coincident nodes

Ex1:Curved shell with a rectangular hole

/ SOLU

ANTYPE, STAT, NEW

NSEL, S, LOC, Y, 0

D, ALL, ALL

ALLSEL

F, 11, FX, 10000

F, 11, FZ, 1000

NSUB, 1

OUTRE, ALL, ALL

SOLVE

FINISH

Ex1:Curved shell with a rectangular hole

underside of the shell (i.e the pressure acts in the +z direction) Since

the geometry and loads are symmetric about both the x and y-axes, we

need to model only one-quarter of the structure The dimensions of the plate and stiffeners are shown in the figure below which shows only one-quarter of the structure The Young's modulus E =7.3x10 4 MPa and the Poisson ratio is 0.33.