Analysis of Double Wishbone Suspension System Components

Coventry University School of Engineering

MSc Dissertation in

Automotive Engineering

ANALYSIS OF DOUBLE WISHBONE SUSPENSION SYSTEM COMPONENTS

Submitted By: MOHD ZAKARIA MOHAMMAD NASlR Project Supervisor: COVENTRY UNI : Dr. GURMAIL SlNGH

KUTKM:

1. Professor Dr. MD. RAZALI AYOB 2. Dr. KHISBULLAH HUDA

3othAugust 2006

ABSTRACT

The durability of automotive components is a critical aspect in the product development. Failure in component will lead to a serious damage not only the design of the component itself, but the entire system of vehicle. In this thesis, a stress study of a critical component was performed based on load prediction from multi-body simulation system for double wishbone suspension system under braking and cornering load cases. First, major coordinate points of front wheel drive Aston Martin Vanquish suspension were measured via computer measuring machine. It was then followed by modelling the suspension system linkages into multi-body system analysis via MSC.ADAMS. Quasi-Static analysis was performed using load profile database to determine the load acting on each component for typical load cases.

Later, these

calculated loads were applied to the FEA stress analysis (MSC.PATRAN/NASTRAN) for a critical component selected in order to predict the maximum stress, stress concentration and displacement. From the results of component load and stress study, 1G braking load cases produces higher forces compare to cornering load case. Although the high-tension force occurred at the lower control arm, this structure generated a low maximum stress with factor of safety 7. Meanwhile, the tie-rod working in compression load produced the highest stress during braking condition which then buckling analysis is performed. However, both components did not exceed the yield stress of the material.

CHAPTER 1

INTRODUCTION

1.1

Introduction

The hnction of suspension system is to absorb vibration due to irregularities of road conditions. Furthermore, it also designed to maximize the friction between tyre contact patch and the road surfaces to provide vehicle stability under any circumstance associated with accelerating, bralung, loaded or unloaded, uneven road, straight line or cornering.. The suspension system significantly affects ride and handling of the vehicle that is 'vibrational' behaviour including ride comfort, directional stability, steering characteristics and road holding. Generally, suspension system can be broadly classified as dependent and independent types. The factor which primarily affect the choice of suspension type at the front or rear of the vehicle are the engine location and whether the front wheels are driven Iundriven and /or steeredlunsteered .

DOUBLE W W B O N E SUSPENSION SYSTEM

Independent suspension (i.e. double wishbone, McPherson and multilink) leads to better ride and handling capabilities [1,3,5].

It is important to analyze the suspension

systems that have been designed to predict the behaviour of the system than followed with improvements. The suspension must be properly designed because it is a crucial subsystem in vehicle in order to: Cany the weight of vehicle and also its weight (unsprung weight). Keep the wheels perpendicular to the road for maximum grip resultant good ride and handling performance. Take the forces for accelerating or braking the vehicle. Ensure that steering control is maintained during manoeuvring. Take the forces involved when cornering the vehicle. Nowadays, the computational power has been developed to make the vehicle dynamics analysis easier with better accuracy and less computing time. MSC.ADAMS (Automatic Dynamic Analysis ofMechanica1 Systems) software is one of tools that widely use as multi-body systems analysis (MBS). It is not only used in automotive industry but other industries like aerospace, construction, electro-mechanical and general mechanical industries. MSC-ADAMS software enables many 'what i f scenarios to be tested quickly without a lot of development testing [2].

1.2

Problem Statement

The factor affecting design for instance to meet the certain performance targets are varying across the range of vehicles. There are also other limitations such as cost, weight, packaging space, requirement for robustness and reliability, manufacturing, assembly and maintenance constraints. For example, sport car such required good ride and handling. Therefore, it has large brake discs, lower arm, tie-rod and wheel knuckle to provide good suspension characteristics. As a consequence, it increase fuel consumption

DOUBLE WISHBONE SUSPENSION SYSTEM

and reduce performances of the vehicle. Moreover, with higher value of unsprung mass could lead the damage to roads surface and increase the vibration. Although many researches have been done to enhance vehicle suspension performance, there are some areas need to be improve using new technique. This research applied new approach where multi-body analysis software (MSC ADAMS) was used to predict the suspension behaviour. For instance cornering and braking load cases which than help the design engineer to do an optimization of the suspension system component. The data input program will develop for double wishbone suspension for 'virtual development process' where reduces the development times, increase model diversity and achieve optimization of the component that has been design. In this work, the author only concentrates on quasi-static analysis of 3D model where a series of static equilibrium solutions depend on time steps requirement. Two different load cases (braking and cornering) have been identified to predict the dynamic load acting on suspension component. Finite element analysis for critical component is then carrying out through MSC PATRAN 1 NASTRAN. The model imported from design tools Solidworks, meshing with 3D-solid tetrahedron elements where the loads in local co-ordinate system determined by multi-body system. The suspension is then modelled and later analyses were done o n braking and cornering load cases input forces respectively. Linear stress analysis will be performed to investigate the maximum stress concentration of each component. In addition, buckling analysis will also performed for the tie rod component to predict whether that component tends to buckle or not.


1.3

Objective and Scope

The objective of this thesis is to analyse in terms of component load and stress study, a quarter vehicle of front wheel drive for typical double wishbone suspension system using multi-body simulation system (MBS) together with computer aided design and analysis environment (CAD & CAE). The scopes of research are as follows:

Determine the co-ordinate system (marker point) of typical double wishbone suspension system using computer measuring machine (Faro Arm) Modelling of the suspension system using data input program into multi-body system analysis (MSC-ADAMS)

Carry out quasi-static analysis for typical load cases (braking and cornering) to predict the load acting on each components Modelling of critical component selected using design tool (Solidworks) prior import into FEA. Further analysis of critical component of suspension system using CAE tool (MSC.PATRAN / NASTRAN) to predict the maximum stress and deformation of the structure.

Figure 1.0

1.4

Austin Martin Vanquish double wishbone suspension system

Research Methodology

The suspension systems in a vehicle play a crucial role to provide ride and handling characteristic. The reason of this research is to study and analyse an independent suspension typically double wishbone suspension system of mid-sized vehicle by using selected loads using virtual 3D model via multi-body system software (MSC. ADAMS). The work began with effort to measure the major co-ordinate points for the real suspension system prior model into multi-body simulation software. The equipment used in this research is the Co-ordinate Measuring Machine (Faro Arm) which is available in the Coventry University. This equipment is used to determine the co-ordinate system (as primary data) for Austin Martin Vanquish double wishbone suspension system.


In the second stage, the data input program for using major develops suspension coordinates points and ADAMS command language program. Quasi-static analysis is to determine load acting on suspension components under braking and cornering conditions using multi-body simulation method (MSC.ADAMS). The use of quasi-static analysis is to simulate the diffusion of loads from tyre contact patch through the suspension system and into the body mounts. This type of analysis is used to represent typical service loads carry out by Proving Ground test. The outputs from these analyses represent the peak loads produced at typical location setting by user such as lower wishbone to body mounts, tie rod connection to wheel knuckle and tyre to ground. A critical component was selected for each load cases based on results from ADAMS simulation in the next stages. Next, the critical component selection was selected based on ADAMS results prior modelled into finite element software via MSC.PATRAN 1 NASTRAN Educational version. Finally the results from multi-body system analysis were used as inputs in finite element analysis in order to predict the structural stress and displacement of the suspension component.

{

Stage 1

- Measure co-ordinate of typical suspension using CMM (Faro Arm)

<=>

1 Stage 2

Running Quasi-Static

- To determine the maximum load

with typical Load cases

acting on components.

Critical component selection-based on results in ADAMS Stage 3

component in FEA

Run Simulation

f

Stage 4

1

El Stress

Figure 1.1

El Buckling

Flow chart of Thesis


1.5

Thesis outline This thesis consists of eight chapters. The introduction of this work is presented in

Chapter 1. This chapter described the problem statements, objectives and scope of the study, research methodology as well as the overall outline of the thesis.

Chapter 2 consists of literature reviews on related subjects concerning this thesis. In this chapter, history of suspension system, the classifications of vehicle suspension systems are reviewed. Review on recently published articles related to multi-body system simulation using MSC.ADAMS and stress analysis via finite element method is also presented. The history of Finite Element Method, how does it works in NASTRAN are presented. Lastly, the displacement method that applied in MSC.NASTRAN is presented.

The equipment used to collect all the required data were presented in Chapter 3. Coordinate measuring machine technique is an appropriate method used to convert data fiom a real model of suspension into a multi-body simulation system. In this chapter, the analysis of a double wishbone suspension system model is presented. Finally, step by step measuring procedures was explained. Chapter 4 describes the basic definition of vector and explained the notations that were being used throughout this work.

The vector theory for double wishbone

suspension is developed to predict the force acting on each component at particular points. This will be further developed using similar model via MSC.ADAMS so that results could be compared. Chapter 5 describes the component loading, degree of freedom and data input program set up prior to running the simulation. Quasi-static analysis is performed to determine the load acting on the components with cornering and braking load cases. Finally, the critical components are selected based on results fiom the multi-body system analysis.

DOUBLE WISHBONESUSPENSION SYSTEM

Chapter 6 describes analysis regarding the Finite Element Method, particularly for the critical component selected (tie rod and lower wishbone). The step-by-step procedures include importing files of both structures, load and boundary conditions, material used and meshing is presented. Linear Static analysis is performed for the critical component selected based on a multi-body simulation (MSC.ADAMS) results. Chapter 7 discusses the results of all testing involving a quarter vehicle of double wishbone suspension systems in a multi body system analysis and a finite element analysis.

This chapter also highlights the suspension behaviour of vehicle during

cornering and braking. Lastly, the graphical results predictions were provided for the tie rod and lower wishbone structures under two 'worst case' scenario a in multi body simulation.

Buckling analysis via classical and simulation method for the tie rod

structure in finite element is also presented. Chapter 8 is the final chapter where conclusion and recommendations were made. It summarizes the work done in the entire study and provides recommendations for future work.


CHAPTER 2

LITERATURE STUDY

2.1

Introduction The Multi Body System analysis using data input programs is often used to

determine the load acting on suspension components. The established loads were then used as data input to finite element models of components or vehicle structure [2,4]. These simulations results can be used to match a series of tests that were performed by many vehicle manufacturers via proving ground test to predict the durability of the vehicle structures. A literature review was conducted to investigate the past research done in many areas related to this work. In addition, histories and theory as well as the main function of multi-body and finite element method were presented.


2.2

Brief history of suspension systems

In the 1 6 ' ~century, researchers tried to solve the problem of 'feeling every bump in the road' of coaches e.g. wagons and carries, by slinging the carriage body from leather straps attached at four posts of a chassis that looked like an unturned table. Because the carriage body was suspended from the chassis, the system came to be known as a 'suspension', and this term still used today to describe the entire class of solution [5]. Gottlieb Daimler in Germany and some European vehicle manufacturers have tried to applied coil springs. However, most manufacturers stood fast with leaf spring which was less costly, easy to produce and assemble to the vehicle. Obadiah Elliot of London invented the venerable leaf spring, which some manufacturers still use in rear suspensions today, in 1804 [24]. He simply piled one steel plate on top of another, pinned them together and shackled each end to a carriage. A Frenchman named J.M.M Truffault fit the first shock absorbers to a racing bicycle in 1898. By 1934, General Motors introduced the coil spring suspension with each tyre sprung independently (independent suspension). After that, most vehicles started using hydraulic shock absorbers and balloon (low-pressure) tyres.

2.3

Function of suspension systems

Suspension is the term given to the system consists of spring, shock absorbers and linkages that connect a vehicle chassis to its wheels. Suspension systems are designed to contribute handling and braking of vehicle. Moreover, the suspension also kept vehicles occupant comfortable and reasonably well isolated from noise, bumps and vibrations.

I

Traditionally, automotive suspension designs have been a compromise between the two conflicting criteria of road holding and passenger comfort. The suspension system must support the weight of the vehicle to provide directional control during or manoeuvres, and also provide effective isolation of passengers as well as payload from road disturbances [8]. Most automobile engineers consider the dynamics of moving vehicles from two perspectives: Ride

-

Handling -

the ability of vehicle to smooth out a bumpy road the ability of vehicle to perform safely during acceleration, braking and cornering

The design of a suspension needs to satisfy a number of requirements whose aims partly conflict due to the different operating conditions such as loaded or unloaded, acceleration or braking, straight running or cornering and uneven road surface [1,6]. The forces and moments that operate in the wheel area must be directed into the body. There are two main categories of suspension system; i) Dependent suspension (i.e. Rigid axle, semi rigid axle, trailing arm) ii) Independent suspension (i.e. Mcpherson, Double wishbone, Multilink) For dependent suspension system, the motion of a wheel on one side of the vehicle is dependent on the motion of wheel on the other side. When one wheel of the vehicle strikes a pothole, the effect is transmitted directly to its partner (wheel) on the other side. This has a detrimental effect on ride and handling of the vehicle [5]. With independent suspension system, the motion of wheel is independent of the other wheel, so that a disturbance at one wheel is not directly transferred to a wheel on the other side. This leads to better ride and handling capabilities.


In this thesis, the author intended to study double wishbone suspension from independent suspension category. A double wishbone in United Kingdom also popular in United Stated, where it is often referred to as Short Long Arm (SLA) [7]. Figure 2.0 shows different types of double wishbone configurations.

Figure 2.0

2.4

Example of independent suspension system [23]

MSC.ADAMS as multi-body simulation software

In automotive industry, predicting of durability performance at the early stage of design through simulation is very important [ l 11. The reason is that it strongly affects on increasing reliability and reduction of weight, costs and product development time. The development of multi-body systems analysis has given new opportunities to design engineers in terms of simulation and analysis. Besides that, these techniques can be applied to the simulation of vehicle kinematics and dynamics, offering the ability to model road loading and vehicle manoeuvres with ever increasing accuracy [13]. These techniques are being developed giving benefits to engineers and ultimately customers through lower cost optimization of components .


Cheon-Soo Jang 1111 presents an interesting method for optimization a lightweight suspension component. He performed a dynamic load analysis using ADAMS to determine the loads prior applied to the FEM stress analysis of the cross member. The method to achieve strain field with respect to each load case via quasi-static analysis which ignoring the inertia effect of mass. Comparisons of the stress and durability results were used for optimization. Study by Murali M.R Krishna [lo] explored the effects of shape optimization techniques for suspension,component. Direct linearization method of MSC.NASTRAN software was performed for optimization of a lower control arm suspension. Static analysis of the model was performed with 3D solid tetrahedron elements to predict the stress distribution on component. Optimization was used to ensure there was a minimal increase of weight in order to reduced stresses. Murali et.al. [9], performed optimisation analysis for Upper Control arm in MSC.NASTRAN using five different load cases provided fiom ADAMS simulation.

2.4.1

MSC. ADAMS history The study carry out by Crolla in 1995 [2,4] identified the main types of computer

tools based that can be used for the vehicle dynamic simulation. He categorised the tools as follows: i) Purpose designed simulation codes ii) Multibody simulation packages based on numerical and algebraic methods iii) Toolkits such as MATLAB The ADAMS program is a typical example of the multibody analysis programs and categorised as numeric where the user is concerned with assembling a physical description of the problem rather than writing equation of motion. Blundell [12]


published papers that summarised the process involved by using ADAMS to simulate full vehicle handling. He described an overview of the usage of multi-body system analysis in vehicle dynamics and followed by suspension modelling and analysis methodologies. He demonstrated in his papers the accuracy of simple efficient models based on design parameters amenable to the sensitivity study. Research initiated by Chase at University of Michigan traced back the origin of ADAMS in 1967. Chase and Korybalski had completed the original version on DAMN (Dynamic Analysis of Mechanical Networks) in 1969. Orlandea completed the first ADAMS program in 1973 and also published two ASME papers (Orlandea et. al., 1976A, 1976B).

This was an earlier development of two-dimensional code to a three

dimensional code without computer capability support called DRAM. In 1980, Mechanical Dynamics Incorporated (MDI) was formed and took responsibility to develop the ADAMS program at University of Michigan. Since 2002, MDI has been part of MSC Software Corporation. The study by Blundell [12] described the behaviour of systems consisting of flexible or rigid parts connected by joints and used large displacement code of motion and in particular the application of ADAMS in vehicle dynamics. Blundell et.al. [13] identified the criteria which would be involved in the decision process in multibody system analysis for instance modelling capability, Pre and Post-processing and analysis modes that would be able to perform. In early 90's, ADAMSNiew was released which allowed users to built, simulate and examine results in a single environment.

2.4.2

Types of simulations in MSC.ADAMS

Static System have DOF > 0 All system velocities and accelerations are set to zero Can fail if the static solution is a too long fiom initial Kinematics System have DOF = 0 Measure the reaction forces in constraints. Driven by constraints (motions)

Dynamic System have DOF > 0 Driven by a set of external forces and excitations Algebraic equations and nonlinear differential can be cnlweA

Figure 2.1

Summary of simulation in MSC.ADAMS [22]

Figure 2.1 shows that multi-body system analysis such MSC.ADAMS has capability to simulate a real model of suspension system or even full vehicle in three basic conditions such as static, dynamic and kinematics analysis. These 'virtual product development' tools can be used to investigate the suspension behaviour and continue further with design and system optimisation.


2.4.3

Standard Joints

There are a few types of mechanical joints can be used to constraint the motion of bodies. Most common joints used in multibody system analysis are shown in Figure 2.2

Revolute

Spherical

Planar

Fixed

Cylindrical

Universal

Translational

Rack & Pinion

Figure 2.2 Examples of constraints joint used in MSC.ADAMS [2]

Modelling the connections between the suspension links will depend on the type of vehicle and suspension position in the vehicle. For instance, lower control arm and wheel knuckle connection can be modelled using spherical joints to represent the balljoints. An example of the syntax used to define a joint and markers in ADAMS is shown below.

PART10I, GROUND PART102, MASS=I ,CM=0200, IP=l ,I, 1 MARKERIO200,QP = 25 1,2OO,lOO,ZP= 400,20,100 JOINTIOI, SPH, I = 0101, J = 0201,


The first statement of this program defines as ground part. Using the system of units used throughout this text, the second statement defines as a part with 1 kg of mass where centre marker located at the position of marker 0200. The IP argument represents three sequential mass moments of inertia in kg.rnrn2 about the x-axis, y-axis and z-axis. In this example, marker 0200 is defined as part 02 and located relative to the local part reference frame of part 01 by the co-ordinates specified through the QP argument. The method used in ADAMS program to use ZP parameter for each marker to represent the local z-axis of the markers. For the universal joint the axes of the spindles need to be defined perpendicular to one another. For other joints such as the revolute, cylindrical and translational, the user have to define the orientation of the axis associated with the mechanical characteristics, rotation and/or translation, of the joint through the coordinates I and J marker.

2.4.4 Degrees of Freedom

The determination degrees of freedom (DOF) in mechanical system started from any free floating rigid body in three-dimensional spaces that have six degrees of freedom.

. VERTICAL

Figure 2.3

Degrees of freedom associated with unconstrained rigid body


Figure 2.3 shows the vehicle produces degree of freedom associated with translational motion in the longitudinal direction X, the lateral direction Y and the vertical direction Z. The rotational motions will involve roll about the x-axis, pitch about the y-axis and yaw about the z-axis. A tyre model will through the forces and moments generate the only contact.

For any multibody systems model where represent the real model, it is important that the user could determine and understand the total degrees of freedom in the system. This can be achieved by using the Gruebler equation as follows: Total DOF = 6 x (Number of parts -1)

- (Number of

constraints)

(2.1)

The degrees of fi-eedom removed by typical constraint elements are surnrnarised in Table 2.0 and also can be used to complete the calculation. Table 2.0 DOF removed by constraint elements [2]

Constraint Element

Translational Rotational Coupled Constraints Constraints Constraints

Total Constraints

Cylindrical Joint Fixed Joint Planar Joint Rack-and-pinion Joint Revolute Joint Spherical Joint Translational Joint Universal Joint

2 3 1 0 3 3 2 3

2 3 2 0 2 0 3 1

0 0 0 1 0 0 0 0

6 3 1 5 3 5 4

Atpoint Joint Primitive Inline Joint Primitive Inplane Joint Primitive Orientation Joint Primitive Parallel Joint Primitive Perpendicular Joint Primitive

3 2 1 0 0 0

0 0 0 3 2 1

0 0 0 0 0 0

3 2 1 3 2 1

Motion (Translational) Motion (Rotational) Coupler

1 0 0

0 1 0

0 0 1

1 1 1

4

uild a model of your design using:

.

Joints Motion generators

+ Contacts

;

i

.

~ e syour t design using: 4

i

j

4

Measures Simulations

4

Animations I Plots

1 validate your model by:

.

Importing test data j ;j + Superimposing test data

:. i'

:I

.JReview your model by adding :

!; I

. . '$,j . +

1

Friction

Flexible parts

!

; ?

i

I Iterate your design through variations using:: Parametrics Design variables

{, Improve .. .. 4

,. :,I>

:.-. ~ "k,

Figure 2.4

.

your design using:

DOES

Optimization

I :, Automate your design process using :

.2; ...->?; : ..--., . . ..-:'s,. :y i L . .;.?.,. -.. SGL. 1 . . (. :

Control systems

1/

/

&;!&+.*%I

.

Forcing functions

+

Custom menus Custom dialog. boxes --

.

Macros

Virtual prototype process applied in MSC.ADAMS [22]


2.4.5 Modelling method

There are two methods used to model the suspension system in MSC.AD Graphic User Interface (GUI) and text programming. I.nouse button to

d i s p l q options.

solid shapes and consnucnon garnotzy

solid features.

M a ~ nToolbox Model name

contalner

Figure 2.5

I

\/iejva tnad

r

Menus

L Status bar

Graphic User Interface (GUI) method in ADAMSI View [22]


The intermediate user usually uses the programming method since the program command language, the coordinates position and behaviour of the model need to be understood fully.

Table 2.1

An example of data input program set up in Notepad for ADAMSI View

DOUBLE WISHBONE SUSPENSION SYSTEMBUSHING ! LOADCASE ;POTHOLE BRAKING

PART10 1,GROUND MARKENO 101,QP=2802,397,l 65,ZP=2500,470, 117 ground MARKENO102,QP=2500,470,117,ZP=2802,397,165 MARKER/O104,QP=2803,3 14,-24,ZP=2418,357,-24 MARKENO105,QP=2418,357,-24,ZP=2803,314,-24 MARKER/0108,QP=2924,307,79 MARKER10109,QP=2798,800,-222 MARKENO112,QP=2700,500,250 MARKEN1,ZP=l ,O,O MARKER/2,ZP=O, 1,O MARKEN3,ZP=O,O, 1

!

2.5 Finite Element Method The finite element (FE) method was developed by engineers using physical insight as opposed to abstract method used by mathematicians [15]. The FE method does not produce a formula as a solution, nor does solve a class of problems. Moreover, the solution is a presentation of the approximation values except for a very simple problem that is congruent with formula that already available.

Wiliam.J.Kroppe et.al. [14] presented the flexibility of the independent suspension components such as lower control arm and wheel knuckle via finite element analysis. He found that the overall forces and stresses have a minor effect in a rigid body


analysis of the suspension components. He also realised that the flexibility analysis was very time consuming to run and CPU intensive.

2.5.1

Short history of Finite Element In 1943, a mathematician, R. Courant, developed a Finite Element Analysis

(FEA). He utilised the Ritz method of numerical analysis and minimization of variational calculus to obtain approximate solutions to vibration systems [23,28]. Courant [17] described a piecewise of polynomial solution for the torsional problem. Shortly thereafter, a paper published in 1956 by R.W Clough, H.C. Martin, M.J Turner and L.J Topp that explored the 'stiffness and deflection of complex structures' which established a broader definition of numerical analysis. The 'finite element' terminology was first used in 1960 [18,19]. Only a few general purpose FE software began to appear in the 1970s due to initial cost and limited computer capabilities. In the mid 1980s, since the cost of computers rapidly declined and also increasing their power capability, FEA has been developed to an incredible precision, complete with colour graphic as well as Pre and Post processors. About 40,000 papers and books regarding the FE method and its applications had been published by mid 1990s [151.

2.5.2 What is Finite Element Method?

The FE method is a numerical approximation method [15,22] to investigate the structures behaviour. Basically, the FE method started by cutting (discretization) a structure into several pieces of elements which depends on problem that describes the behaviour in each element in a simple way. After that, the elements are connected to each other at 'nodes'. The assembly of elements and nodes is called a finite element


model [22]. This process produces a set of simultaneous algebraic equations. For the stress analysis, these equations are equilibrium equations of the nodes where may require computer implementation due to thousand of equations generated. 2D and 3D modelling are two types of analysis generally used in industry [28].

2.5.3

How does FEM works in MSC.NASTRAN FEA uses a complex system of points called nodes which make a grid called mesh.

This mesh is programmed to contain the material and structural properties which define how the structure will react to certain loading. A structure model is discretised by dividing the original domain into simply shaped elements which connected to one another by nodes. Each node is capable of moving in six degrees of fi-eedom (DOF) as shown in Figure 2.6

Three translations ( ux ,u,, u, ) Three rotations ( Ox,e,, 8, ) {u) = displacement vector =

{ ux uy uz e x ey8 z 1

.

Figure 2.6

Capabilities of nodes moving in six DOF

The relationship between one element and its surrounding nodes can be described by the following equation:

Analysis of Double Wishbone Suspension System Components

Recommend Documents