ANSYS_Tutorial_eng.pdf

Tutorial

Release 6.1

Kent L. Lawrence

Mechanical and Aerospace Engineering

University of Texas at Arlington

________

SDC

Schroff Development Corporation

www.schroff.com

www.schroff-europe.com

ANSYS ®

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2-1

Lesson 2

Plane Stress

Plane Strain

2-1 OVERVIEW

Plane stress and plane strain problems are an important subclass of general three-

dimensional problems. The tutorials in this lesson demonstrate:

Solving planar stress concentration problems.

Evaluating potential errors in the solutions.

Using the various ANSYS 2D element formulations.

2-2 INTRODUCTION

It is possible for an object with arbitrary shape to have six components of stress when

subjected to three-dimensional loadings. When referenced to a Cartesian coordinate

system these components of stress are:

Normal Stresses

x , y , z

Shear Stresses

xy , yz , zx

Figure 2-1 Stresses in 3 dimensions.

In general, the analysis of such objects requires three-dimensional modeling as discussed

later in Lesson 4. However, two-dimensional models are often easier to develop, easier to

solve and can be employed in many situations if they can accurately represent the

behavior of the object under loading.

2-2

ANSYS Tutorial

x , y , and

xy lie in the X-Y plane and do not vary in the Z direction. Further, the stresses z , yz ,

and

zx are all zero for this kind of geometry and loading. A thin beam loaded in it plane

and a spur gear tooth are good examples of plane stress problems.

ANSYS provides a 6-node planar triangular element along with 4- and 8-node

quadrilateral elements for use in the development of plane stress models. We will use

both triangles and quads in solution of the example problems that follow.

2-3 PLATE WITH CENTRAL HOLE

To start off, let’s solve a problem with a known solution so that we can check our

understanding of the FEM process. The problem is that of a tensile-loaded thin plate with

a central hole as shown in Figure 2-2.

Figure 2-2 Plate with central hole.

= 2.07 x 10 11 N/m 2 and

Poisson’s ratio, = 0.29. We apply a horizontal tensile loading in the form of a pressure

p = 1.0 N/m 2 along the vertical edges of the plate.

Because holes are necessary for fasteners such as bolts, rivets, etc, the need to know

stresses and deformations near them occurs very often and has received a great deal of

study. The results of these studies are widely published, and we can look up the stress

concentration factor for the case shown above. Before the advent of suitable computation

methods, the effect of stress concentration geometries had to be evaluated

experimentally, and many available charts were developed from experimental results.

A state of Plane Stress exists in a thin object loaded in the plane of its largest

dimensions. Let the X-Y plane be the plane of analysis. The non-zero stresses

The 1.0 m x 0.4 m plate has a thickness of 0.01 m, and a central hole 0.2 m in diameter.

It is made of steel with material properties; elastic modulus,

Plane Stress / Plane Strain

2-3

The uniform, homogeneous plate above is symmetric about horizontal axes in both

geometry and loading. This means that the state of stress and deformation below a

horizontal centerline is a mirror image of that above the centerline, and likewise for a

vertical centerline. We can take advantage of the symmetry and, by applying the correct

boundary conditions, use only a quarter of the plate for the finite element model. For

small problems using symmetry may not be too important; for large problems it can save

modeling and solution efforts by eliminating one-half or a quarter or more of the work.

Place the origin of X-Y coordinates at the center of the hole. If we pull on both ends of the

plate, points on the centerlines will move along the centerlines but not perpendicular to

them. This indicates the appropriate displacement conditions to use as shown below.

Figure 2-3 Quadrant used for analysis.

In Tutorial 2A we will use ANSYS to determine the maximum stress in the plate and

compare the computed results with the maximum value that can be calculated using

tabulated values for stress concentration factors. Interactive commands will be used to

formulate and solve the problem.

2-4 TUTORIAL 2A - PLATE

Follow the steps below to analyze the plate model. The tutorial is divided into separate

Preprocessing, Solution, and Postprocessing steps.

PREPROCESSING

1. Start ANSYS and select 'Interactive'; select the Working Directory where you will

store the files associated with this problem. Also set the Jobname to Tutorial2A or

something memorable. Then select Run.

Select the six node triangular element to use for the solution of this problem.

2-4

ANSYS Tutorial

Figure 2-4 Six-node triangle.

2. Main Menu > Preprocessor > Element Type > Add/Edit/Delete > Add >Solid >

Triangle 6 node 2 > OK .

Figure 2-5 Element selection.

Select the option where you define the plate thickness.

3. Options (Element behavior K3) > Plane strs w/thk > OK > Close

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