SCHOOL OF CIVIL ENGINEERING

STRUCTURAL ENGINEERING

ACADEMIC SESSION 2014/2015

EAS 661 ADVANCED STRUCTURAL MECHANICS

(ASSIGNMENT)

NAME : NAQIYATUL MISKA

MATRIC NO : P-WM0016/14

MODELLING PLANE STRESS AND PLANE STRAIN PROBLEM IN LUSAS

ANALYST

Introduction

In the real world, the structure are three dimensional and even has a complex shape which

hard to analyse. To make it easiser, the structure should be devide into lots of smaller and

simple shapes. This method is called Finite Element Analysis (FEA). Another approch is

by just analyse one part of the structure if it can be a representation of the whole

structure. This assumption only if the structures geometry and load can be completely

describe in one plane.

One of FEA software that is used worldwide is LUSAS. In this report, LUSAS will be

used to analyse a 5 mm thick steel plate with dimension 500 mm 100 mm, and 50 mm

diameter hole located at the centre. A 100 N/mm2 stress is applied at both end of the plate

in x-direction. The material is mild steel with Modulus of Elasticity (E) 200 Gpa, and

poisson ratio 0.3.

The plate will be analyse into two condition, plane stress condition and plane strain

condition. The result that is obtained are stress and strain distribution.

FE modelling

The analysis is done for a quater of the plate as shown in the picture.

Figure 1 : a quarter plane

The model then devide into three area. Meshing is defined with structural element type

are plane stress or plane strain, and element shape is quadrilateral and size is 5 mm.

Interpolation order is linear.

Figure 2 : Three area after meshing

Material is defined as mild steel with E=200Gpa, and poisson ratio 0.3. Support condition

are define into 2 kind. Support 1 located at the upper left y-direction line for plane stress

condition translation in x,y, and z direction are fixed, free, free and rotion in x,y,z

direction are free, fixed, and fixed. For plane strain translation in x,y,z direction are fixed,

free, fixed, and rotation in x,y,z direction are free, fixed, fixed. And the Support 2

condition located at lower x-direction line for plane stress translation in x, y, and z

direction are free, fixed, free and rotation in x, y, z direction are fixed, free, fixed. For

plane strain condition, translation in x, y, z direction are free, fixed, fixed, and rotation in

x,y,z direction are fixed, free, and fixed. A 500 kN/mm loading is assigned at the rigth y-

direction line. The direction of the loading is same as x-direction.

Figure 3 : Complete assignment

Result and Discussion

Plane Stress condition

Figure 4 : Stress distribution in x-direction

Figure 5 : Stress distribution in y-direction

The figures shows the distribution of stress in x and y direction. The colour indicate stress

intensity which blue and green colour indicate the lower value of stress and yellow, orange and

blue colour indicate the higher value of stress. The maximum value of stress in x direction is

428.2 and in y-direction is 48.34 both located near the hole edge. It can be conclude that the

critical part of the plate located at the boundary of the hole.

Figure 6 : Strain distribution in x-direction

Figure 7 : Strain distribution in y-direction

The maximum strain value for plane stress condition in x-direction is 0.2037E-02 and in y-

direction is 0.4139E-04. The maximum strain distribution also located at the hole boundary.

Plane Strain condition

Figure 8 : Stress distribution in x-direction

Figure 9 : Stress distribution in y-direction

For plane strain, the maximum value of stress in x-direction is 2146 and in y-direction is 242.7.

The higher value of stress is distributed at the hole boundary, which indicated that this part is the

most critical part.

Figure 10 : Strain distribution in x direction

Figure 11 : Strain distribution in y-direction

The maximum value of strain in x-direction is 0.3408E-03 and in y-direction is -0.4046E-02,

also located at the critical part near the hole boundary.

The summary that can be made is, this two model condition has different kind of stress acting on

the critical part. The plane stress condition got the lower stress value than the plane strain

condition. Correspondently, the strain also got the higher value in plane strain condition. In can

be conclude that this model is better to be used in plane stress condition which result in lower

stress and strain value than if it used in plane strain condition.