EXAMPLES OF TWO-DIMENSIONAL ELEMENTS IN ANSYS
ANSYS offers many two-dimensional elements that are based on linear
and quadratic quadrilateral and triangular shape functions. Some
examples of two-dimensional structural-solid and thermal-solid elements
PLANE2
is a six-node triangular structural-solid element. The element has
quadratic displacement behavior with two degrees of freedom at each
node, translation in the nodal x -and y-directions.The element input data
can include thickness if KEYOPTION 3 (planestress with thickness
input) is selected. Surface pressure loads may be applied to element
faces. Output data include nodal displacements and element data, such as
directional stresses and principal stresses.
PLANE35
is a six-node triangular thermal solid element. The element has one
degree of freedom at each node, the temperature. Convection and heat
fluxes may be input as surface loads at the element faces. The output
data for this element include nodal temperatures and element data, such
as thermal gradients and thermal fluxes.
PLANE42
is a four-node quadrilateral element used in modeling solid problems.The
element is defined by four nodes, with two degrees of freedom at each
node, the translation in the x- and y-directions.The element input data
can include thickness if KEYOPTION 3 (plane stress with thickness
input) is selected. Surface pressure loads may be applied to element
faces. Output data include nodal displacements and element data, such as
directional stresses and principal stresses.
PLANE55
is a four-node quadrilateral element used in modeling two-dimensional
conduction heat transfer problems. The element has a single degree of
freedom, the temperature. Convection or heat fluxes may be input at the
element faces. Output data include nodal temperatures and element data,
such as thermal gradient and thermal flux components.
PLANE77
is an eight-node quadrilateral element used in modeling two-dimensional
heat conduction problems. It is basically a higher order version of the
two-dimensional, four-node quadrilateral element PLANE55. This
element is more capable of modeling problems with curved boundaries.
At each node, the element has a single degree of freedom, the
temperature. Output data include nodal temperatures and element data,
such as thermal gradient and thermal flux components.
PLANE82
is an eight-node quadrilateral element used in modeling two-dimensional
structural solid problems. It is a higher order version of two-dimensional,
four-node quadrilateral element PLANE42. This element offers more
accuracy when modeling problems with curved boundaries. At each
node, there are two degrees of freedom, the translation in the x- and ydirections.The element input data can include thickness if KEYOPTION
3 (plane stress with thickness input) is selected. Surface pressure loads
may be applied to element faces. Output data include nodal
displacements and element data,such as directional stresses and principal
stresses.
EXAMPLE
Consider one of the many steel brackets (E = 29 x l06 lb/in2,v = 0.3) used
to support bookshelves. The dimensions of the bracket are shown in
figure. The bracket is loaded uniformly along its top surface, and it is
fixed along its left edge. Under the given loading and the constraints,
plot the deformed shape; also determine the principal stresses and the
von Mises stresses in the bracket.
The following steps demonstrate how to solve this problem using
ANSYS:
Enter the ANSYS program by using the Launcher.
Type Bracket (or a file name of your choice) in the Initial Jobname
entry field of the dialog box.
utility menu: File + Change Title (Write Bracket)
Define the element type and material propcrties:
Main Menu: Preprocessor + Element Type + Add/Edit/Delete
Select PLANE82
Options -> Select Plane Stres with Thickness
Assign the thickness of the bracket:
main menu: Preprocessor + Real Constants
Write 0.125 as thickness
Assign the modulus of elasticity and the Poisson's-ratio values:
main menu: Preprocessor + Material Props + -Constant-Isotropic
E = 29 x l06 lb/in2,v = 0.3
main menu: Preprocessor + Modeling-Create + Areas-Rectangle + By 2
Corners
You are now ready to mesh the area of the bracket to create elements and
nodes. Issue the commands
main menu: Preprocessor + -Meshing-Size Cntrls + -Manual SizeGlobal-Size (give 0.25)
Then issue the commands
main menu: Preprocessor + -Meshing-Mesh + Areas-Free +
Click on the Pick All button.
Apply boundary conditions:
main menu:Solution + Apply + Structural- Displacement on Keypoints
(Select left two keypoints and Select Alldof)
main menu:Solution + Loads-Apply +Structural-Pressure+ On Lines +
Pick the upper two horizontal lines associated with Area 1 and Area 2
(on the upper edge of the bracket).
(give 10)
Solve the problem:
main menu: Solution + -Solve-Current LS
OK
Close (the solution is done!) window.
Close (the STAT Command) window.
For the postprocessing phase, first plot the deformed shape by using the
commands
main menu: General Postproc -+ Plot Results -+ Deformed Shape . . .
Plot the von Mises stresses with the commands
main menu: General Postproc + Plot Results + Contour Plot + Nodal
Solution
CW
The bicycle wrench shown in Figure is made of steel with a modulus of
elasticity E = 200 GPa and a Poisson's ratio v = 0.32. The wrench is 3
mm thick. Determine the von Mises stresses under the given distributed
load and boundary conditions.