Glass Squash Court Analysis Engineering Essay

The intention of this proposal was to testing the trinquete for Prospec LTD. The trinquete is a special court for indoor ball games and games played in trinquete are very similar to squash. This testing assess whether the product is structurally suitable for use in ball game courts. Their critical failure modes were to be established in order to assess and improve upon the design. World squash federation recommends using of safety glass in situations where a risk of human impact can result.

Around 30 years ago, in Sheffield the glass company by name Ellis Pearson produced the first glass back wall for a squash court. But in the 80's along came chemical giant ICI and produced a Perspex (plastic) court and suddenly glass was too heavy and uneconomical. So Ellis Pearson (now going under the name of Prospec) forgot their roots and started using Perspex. (Ref: GLOBAL GALLERY June 2003, Martin Bronstein's astigmatic view of the world of squash)

Prospec Ltd offers a complete range of squash court packages including wet plaster and dry panelled surfaces, flooring and the Ellis Pearson Glasswall system. Prospec is considered to be the market leader in the UK for the supply and installation of World Squash Federation (WSF) approved squash courts and Glasswalls. Prospec have installed more than 30,000 Ellis Pearson Glasswalls round the world for Squash, Racquetball and Pelota.

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Prospec LTD manufactures toughened glass squash courts that meet the stringent specifications of the World Squash Federation. This glass carries WSF certification for both two and four panel backwall systems. Prospec Toughened Safety Glass meets the performance requirements of all national building regulations, based on test requirements of local authorities as well as the WSF.

Installation of these glass walls is carried out by operatives trained by Prospec Court Systems Ltd., either direct or through Contractors who specialise in fitting out squash courts. Installation will be done according to the world squash federation technical standards.

Introduction

For centuries people have played games that involve hitting balls with racquets against wall or back and forth to each other across a net. The most common example is tennis. In 19th century the prisoners were exercised by making them hit small and hard ball around the walls of a large room in the Fleet prison in London, England. A trinquete is a special court for various indoor versions of Pelota (Spanish for ball). It has the same characteristic feature of a squash court.

The Pelota is a traditional sport played in more than 52 countries. Pelota is a name for a variety of court sports played with a ball using one's hand, a racquets, a wooden bat or a basket against a wall. These game is played by two or four players, with two team face to face separated by a line on a ground or a net. Today, Pelota is widely played in several countries: in the Basque Country and their neighbours; in Valencia where it is considered the national sport; and in rural areas of Ireland, Belgium, North of Italy, Mexico, Argentina and other American countries.

The reason for the dramatic growth of these type games is because these sports combine fitness, fun and competition. This is an international sport played between two or four players in a four walled court with a small hollow rubber ball by hitting rubber ball against walls. The players strike the ball alternately on to the front wall, which is 4.75 meters high. Players can hit the ball directly to the front wall or use the sidewalls and rear wall to create subtle winning shots.

Playing squash type games develops speed, endurance, agility, coordination and court savvy. The average length of the game is less than 45 minutes. The popularity of the game is due in large part to the competitive workout it generates in a small span of time. These games are simple to learn and it's difficult to master. The challenge is to achieve goal against more skilled opponent and you'll play as you improve. This game is mentally and physically draining and at the end of the day you will be satisfied and exhilarated and possibly a little tired.

A trinquete is a special court for various indoor versions of Pelota. Trinquete measures 28.5m long and it has different shape than the other courts, with an inclined roof along the left wall. Left wall of the trinquete is constructed by toughened glass. Trinquete is constructed by many materials providing suitable rebound and safe to play; however, the World Squash Federation publishes court specification which recommends standards.

Types of wall systems:

(Ref: http://www.andersoncourts.com/wall.htm)

1) Armourcoat hard plaster: is 100% gypsum based plaster system formulated with high impact resistance. This is been installed in over 40 countries and accreditation with world squash federation. This system contains no cement based product, hence eliminating shrinkage and stress cracking. The total system thickness is 12.7mm consisting of 2 layer of base coat plaster and 3 layers of finish coat plaster which is applied on wet for permanent bond and smooth finish. Armourcoat requires no painted finish, finished coat available in blue, green, white and yellow colour. Armourcoat walls can be cleaned using household, non-abrasive cleaners with scouring pads and rinse with clean water.

2) Doweloc edge grain: is superior in quality and durability, longevity proven is 60+ year's court and still in play. Doweloc is a Northern hard maple; edge grain system consists of tongue and groove wood strips held securely by the aluminium dowel. Each 12inch section is composed of 14 edge grain pieces. Walls are then painted to secure wood based on the usage of the court.

3) High density fiberesin panel: is the pre - finished playing surface and engineered specifically for racquetball, handball and squash courts. It is a solid and rock hard sheet material used to meet a rigid specification and requirements demanded for the fast action sports court. It is composed of high density particle board cores and multiple layers of thermalset resin impregnated sheets that are moulded in hydraulic presses under controlled heat and pressure into sheets of varying thickness and density. Fiberesin requires no refinishing and only occasional washing.

Glass walls: is a substitute for the walls which been mentioned above, since 1980's guaranteeing to meet world squash federations high technical standards. Glass walls are transparent, so it makes game visible for spectators. Walls must not only be transparent, it has to be tough enough to rebound the hard ball without breaking. Since normal glass is not hard to withstand the pressure of the ball toughened glass is used. Toughened or tampered glass is very much strong and satisfies all the standards of world squash federation, like strength, transparency and safety etc.

The 12mm toughened glass panels are designed to provide a flush finish and easy panel adjustment and alignment. The panels are joined by special patch fittings and 15mm thick glass fins. Joints between the glass panels are filled with a clear silicone sealant, to complete the continuity of the glass and ensure a true playing surface that is tough enough to withstand pressure from either ball or player. This joint configuration distributes and reduces stresses, minimizes deflection, vibration or damage, and provides true ball rebound.

Toughened glass

Toughened glass is much stronger than normal glass, having been processed by controlled thermal or chemical treatments to increase its strength. Toughened glass is impact resistant, and it is made from annealed glass which is heated and then rapidly cooled. Thermally toughened safety glass offers first order mechanical characteristic. This is the only glass exhibits well establishment and reliable mechanical capacity under static and dynamic load with resistance to impact properties conforming to regulations and European standards. The glass usually shatters into small fragments instead of sharp shards when broken, making it less likely to cause severe injury and deep lacerations. Toughened glass is used in a variety of applications as a result of its safety and strength. (ref: Toughened Glass: Mechanical Properties and EN 12600 Behaviour

Michel Dubru, Glaverbel S.A. Jean-Clement Nugue, Saint-Gobain Guy Van Marcke de Lummen, Glaverbel S.A)

The manufacture of toughened glass

Flat glass is toughened in an oven, the glass is transported on rollers and in rolled back and forth inside oven and heated in a temperature between 600 and 700°c until glass become soft. A softened glass is rolled out of the oven into air shower where both the side of the glass is cooled rapidly. The inside of the glass is hot and soft while the outer surface of the glass cool, solidify and contract due to thermal contraction. After this the inside glass cool, solidify and contracts. The outer surface is already cold when the inner region begins to solidify, so contraction in the inner region squeezes the outer surfaces. Hence the region near the outer surface experiences high compressive force and which is balance by the tensile force generated at the inner surface. The toughening process produces a safety glass which is very strong. The rapid cooling places the internal stresses on the glass which allow it to be strong and break into regular cubes. Due to the internal stresses the toughened glass cannot be broken into the required dimension, therefore all shapes will be done before the toughening process.

Toughened glass surface is more resistant to impact. The same object thrown would create a hole in a pane of annealed glass would likely bounce back when compared to toughened glass. Because of this impact resistant and bouncing nature, toughened glass is used in trinquete and squash courts. (ref: www.picams.com.au/.../Toughened%20glass%20-%20with%20an%20achilles%20heel.pdf)

DATA TABLE:

Mechanical Properties

Quantity

Value

Unit

Young's modulus

50000 - 100000

MPa

Bending strength

200 - 200

MPa

Physical Properties

Quantity

Value

Unit

Thermal expansion

9 - 9

e-6/K

Thermal conductivity

0.9 - 0.93

W/m.K

Specific heat

840 - 850

J/kg.K

Melting temperature

1100 - 1100

°C

Service temperature

0 - 700

°C

Density

2500 - 2800

kg/m3

Resistivity

1e+18 - 1e+18

Ohm.mm2/m

Environmental Data

Quantity

Value

Unit

Ex (in) / Ex (out)

38.1609195402299

MJ/MJ

Remark: Has to be made to measure before hardening. Available in 4, 5, 6, 8, 10 and 12mm thickness

(Ref: http://www.matbase.com/material/glass/toughened-glass/thermal/propertie)

RECOMMENDED STANDARDS OF CONSTRUCTION

(Ref: http://www.worldsquash.org/uploads/Court%20Specs%20-%20With%20Diagrams.pdf)

International Squash court has been constructed from glass or transparent materials, to make game visible for the spectators. Spectator areas may be located behind the plane of any wall of the court.

The play is televised, filmed, photographed or recorded from above the court or through any of the walls. No camera or any equipment is projected into the court or below the clear height of the court. Camera panels may be incorporated in any part of the court playing walls provided that any such panel shall.

Court dimensions and tolerances: is the important standard which has to be taken into account. The length of the court is 28500mm and with tolerance of plus or minus 10mm.

The Court Walls should be vertical to within plus or minus 5mm in a height of 2 metres when measured within 250 mm of each corner of the court and at three additional intermediate points evenly spaced along the length of each wall.

The court walls shall be straight to within plus or minus 15 mm in the length of any wall when measured horizontally at a height of 1 metre above finished floor level.

The floor shall be level to within plus or minus 10 mm in the length, width and on the diagonals of the court.

The walls of the court and all the components should be capable of withstanding all the stresses due to impact of the ball, racquet and the player, and glass must get permanent or temporary damage. Mass of the player should be considered, glass might be damaged when the player falls on the wall. The mass of the player is equivalent to 100kg and co-efficient of absorption is 47 %( i.e. 47% of the impact energy is observed by the body and remaining 57% energy will be transmitted on the wall).

Where courts have transparent walls they shall be constructed of safety materials tested in accordance with the appropriate national standard and shall meet the stated requirements for safe breakage.

The walls of the court must not deflect for the impact of the ball in such a manner that rebound of the ball is affected. The walls may deflect under the impact of players; however, it should not deflect to such an extent or in such a manner so as to affect the safety of the players. The wall which deflects shall return back to its original static position within one second of the impact, as a result of deflections the wall must not suffer from any permanent and temporary damages.

All walls of the court shall have a hard and smooth finish. Any front or side walls, or any transparent panel in the playing surface of the front or side walls, shall be treated and/or lit in such a manner as to make it non-reflecting when viewed from inside the court.

The average reflectance of the front and side walls shall not be less than 50% at any point when in a clean condition. The reflectance of the front and side walls shall not vary at any point by more than plus or minus 5% of the average reflectance.

The ball shall rebound truly on striking all parts of the playing walls. The ball rebound shall be consistent over the whole area of each wall. All wall surfaces including transparent materials shall have surface friction such that the pace and wall angle characteristics are equivalent to that encountered in a plaster court.

Any open joint in the finish of a wall of panel construction shall not deflect the rebound of the ball in any way.

There shall be no protrusions of any kind into the court at the junction of one wall with another.

The bounce of the ball shall be of even height and pace over the whole area of the floor. When viewed from vertically above the line of flight of the ball, the linear path of the ball shall not be affected when it bounces on the floor.

SPECIFICATIONS

www.worldsquash.org/.../Court%20Specs%20-%20With%20Diagrams.pdf

GLASS

All walls and fins are 12mm clear tempered or toughened glass with finished edges. All holes on the playing side are countersunk and dimensioned to receive special flush mounted fittings and hardware. A clear silicone compound is used to bond all joints. No glass-to-glass or glass-to-metal contact is permitted.

FITTINGS

All glass-to-glass connections are manufactured in hi-tensile GSM Nylatron. Nylatron GSM is a cast and partially cross-linked. Nylatron GSM is manufactured by modifying Nylon 6 material by a carefully controlled level of finely divided particles of molybdenum disulphide additive. The molybdenum disulphide enhances its bearing and wear behaviour without impairing the impact and fatigue resistance inherent to unmodified cast nylon grades.

All parts are moulded for maximum strength. These parts will have tensile strength of 773 to 984 kg/cm² with Hardness durometer of 2.3 and Shear strength of 541 to 668 kg/cm².

Base angle brackets which is been used to fix wall to the floor and are available in either steel or anodized aluminium. Size of the brackets will be 12" x 3" x 2 1/2" x 1/4".

Two anchor bolts of 11mm dia. x 89mm are used for each angle bracket.

Aluminium channels of size 25 x 25 x 3mm and Aluminium angles of size 50 x 50 x 6mm are used to hold panels and attached to fins.

MANUFACTURERS OF GLASS WALLS

(Ref: England squash and racketball, technical information sheet number 1, march 2010)

Complete glass wall systems, court doors, view windows and moveable glass walls as supplied by many glass manufacturing companies. The glass wall is supported by glass fins, aluminium L angle, aluminium posts, or aluminium tube frame. World Squash Federation (WSF) is the governing body for the game of Squash and racquetball throughout the world and is therefore responsible for setting standards for courts and equipment. In order to continue the process of ensuring that courts are built to appropriate standards, it has introduced a scheme whereby materials and components may be tested against the standards set by the Federation.

The WSF assess the manufacturer based on the following criteria:

Court must be easy to install

Suitable performance characteristics

Reliability

Ease of maintenance

Efficiency of back u service

Court contractors

The companies listed below will liaise with the architect & builder regarding the background surface requirement prior to fitting out.

COMPANY

ADDRESS

SYSTEM/TRADE NAME

SQUASH & LEISURE SERVICES

Tel:(01895) 450800

Fax: (01895) 450801

email:info@squashandleisure.fsnet.co.uk

Web: www.squashandleisure.co.uk

5 Sarum Complex

Salisbury Road

Uxbridge UB8 2RZ

Contractor

PROSPEC LTD

Tel: (01709) 377 147

Fax: (01709) 375 239

email: mailbox@prospect.co.uk

P O Box 48

Canklow Meadow Estate

West Bawtry Road

Rotherham S60 2XP

Contractor

COURTCRAFT LTD

Tel: (01942) 881500

Fax: (01942) 881501

email: squash@courtcraft.co.uk

www.courtcraft.co.uk

Logic House

31 Gibfieid Park Ave

Gibfield Business Park

Atherton

Manchester M46 0SY

Contractor

Prefabricated court systems

COMPANY

ADDRESS

SYSTEM/TRADE NAME

ASB CONSTRUCTION LTD

Tel: (01548) 580669

email: asbuk@aol.com

www.asbsquash.com

Huccombe House

Huccombe

Kingsbridge

Devon TQ7 2EP

Self‑supporting sand filled system plus a wall lining system. A sliding wall system is also available. Rainbow coloured court system.

PROSPEC COURT SYSTEMS LTD.

Tel: (01709) 377147

Fax: (01709) 375239

email: mailbox@prospec.co.uk

P O Box 48

Cranklow Meadow Estate

West Bawtree Road

Rotherham S60 2XP

Respatex Squash Court Panel System (prefabricated)

Wall plasters

COMPANY

ADDRESS

SYSTEM/TRADE NAME

ARMOURCOAT LTD

Tel: (01732) 460668

Fax: (01732) 450930

email: mailbox@armourcoat.co.uk

Morewood Close London Road Sevenoaks

Kent TN13 2HU

Armourcoat Hard Court Plaster (white).

REBOUND INTERNATIONAL LTD

Tel: (0161) 929 7758

Fax: (0161) 929 7786

Mob: 07818 046464

email: rebound@copley.co.uk

Copley Square

Charter House

Woodlands Road

Altrincham

WA14 1HF

Rebound Plaster (white)

Flooring contractors

COMPANY

ADDRESS

SYSTEM/TRADE NAME

V A HUTCHISON FLOORING LTD

Tel: (01243) 841175/841127

Fax: (01243) 841173

email: vahutchisonflooring@btinternet.com

Units 1,2 & 3

Building NA

Beeding Close

Southern Cross Trading Estate

Bognor Regis

West Sussex PO22 9TS

Flooring Contractors Maple & Beech & New Levelling System & Cross Batten System

Glass walls

COMPANY

ADDRESS

SYSTEM/TRADE NAME

PROSPEC COURT SYSTEMS LTD

Tel: (01709) 377147

Fax: (01709) 375239

email: mailbox@prospec.co.uk

PO Box 48

Canklow Meadows Estate, West Bawtry Road, Rotherham S60 2XP

Ellis Pearson Glasswall System

SQUASH & LEISURE SERVICES LTD Tel: (01895) 450800

Fax: (01895) 450801

email: info@squashandleisure.fsnet.co.uk

5 Sarum Complex

Salisbury Road

Uxbridge UB8 2RZ

S&LS Glasswall System

FINITE ELEMENT ANALYSIS

Finite Element Analysis (FEA) is the most important tool for the mechanical design engineer. The desire for more accurate design in complex situations is the reason for the development of FEA, and allowing improvement in both design procedures and products. The growing demand of FEA has made possible for the creation of computation engines which are capable of handling the huge volume of calculations and carryout analysis and display results. FEA is now available at a practical cost to virtually all engineers and designers.

Pro/Mechanica offers much more than simply an FEA engine. Pro/Mechanica is one of the modules of pro-engineer, which is widely used to understand structural and thermal product performance. Moreover, unlike many other commercial FEM programs where determining accuracy can be difficult or time consuming, Pro/M will be able to compute results with some certainty as to the accuracy. This saves cost, time and physical prototyping. By studying the product behaviour in early stage, we can improve quality and time, cost and efforts. In todays competitive market the design team is forced to get the product right at first time. When the team has to rely on prototype models to test product behaviour, schedule and budget has to be compromised. Standalone CAE offers a solution but it's usually disconnected with CAD solutions, hence engineers have to spend lot of time in preparing prototype models for analysis. Then each time there could be design change and have to repeat the process. Special skill sets are required for CAE users. Pro/ Mechanica is the faster and smart way to analysis the product and easy to use the solution.

In Pro/Mechanica we can identify where the higher stress area is and any changes in model design can be done to avoid the concentration of the stress and failure of the product. One best part in Pro/Mechanica is once we identify the problem, we are allowed to change the design and regenerate and analyse again. This saves lot of time and efforts to reproduce the design. Pro/Mechanica has an ability to evaluate the product performance virtually; onscreen and this gives an engineer to explore new ideas and then optimize their design. This gives a confidence to an engineer and fewer changes may require during prototyping, hence delivering superior quality to the market.

Steps in preparing FEA model for solutions

There are several steps to be followed in the analysis, starting from the simplified geometric model.

1. Identify the model type

2. Specify the material properties, model constraints, and applied loads

3. Discretize the geometry to produce a finite element mesh

4. Solve the system of linear equations

5. Compute items of interest from the solution variables

6. Display and critically review results and, if necessary, repeat the analysis

Create geometry with PRO/E

Model type

Simulation parameters: Material property

Constraints

Loads

Discretize model to form finite element mesh

Setup and solve linear system

Compute results

Review

The overall procedure is illustrated in the above figure. The steps must be executed in order, and each must be done correctly before proceeding to the next step.

The steps shown in the figure are:

1. The geometric model of the part is created using Pro/ENGINEER.

2. The model type must be identified before entering Pro/Mechanica. The default is a solid model.

3. This is an important step where we need to define parameters.

Specify material properties for the model. All the elements will not have the same properties. The different parts can be made of different materials in an assembly. Young's modulus and Poisson's ratio must be known for stress analysis. Pro/Mechanica consists of set of materials in the library, which can be directly used to assign material.

Identify the constraints on the solution. In stress analysis, there could be fixed points, points of specified displacement, or points free to move in specified directions only.

Specify the applied loads on the model, like loads on surface, edges etc

4. Once all the above steps are completed, we can set up and run a processor that actually performs the solution to the posed FEA problem. This starts with the automatic creation of the finite element mesh from the geometric model by a subprogram within Pro/M called AutoGEM. Pro/M will trap some modelling errors here. The processor will produce a summary file of output messages which can be consulted if something goes wrong - for example, a model that is not sufficiently constrained by boundary conditions.

5. FEA produces immense volumes of output data. The only feasible way of examining this is graphically. Pro/M has very powerful graphics capabilities to examine the results of the FEA - displaced shape, stress distributions, mode shapes, etc. Hard copy of the results file and screen display is easy to obtain.

6. Finally, the results must be reviewed critically. In the first instance, the results should agree with our modeling intent. For example, if we look at an animated view of the deformation, we can easily see if our boundary constraints have been implemented properly. The results should also satisfy our intuition about the solution (stress concentration around a hole, for example). If there is any cause for concern, it may be advisable to revisit some aspects of the model and perform the analysis again.

Benefits:

Pro-engineering Mechanica gives the clear picture of the product performance, and discovers design flaws at early stage. This helps a designer to make any changes in the design and deliver superior quality at first time.

Improves user efficiency with an intuitive, familiar user interface

Mechanica gives realistic performance solutions and this data can be used to improve the quality of the product by directly applying real world conditions to design geometry.

There is lot of limitation in analysing physical prototype; these are overcome by Mechanica in which more scenarios can be evaluated.

This save lot of time by avoiding prototypes and analysis time is very less when compared to any other type. Mechanica reduce errors by working in a seamlessly integrated design and simulation environment with no data translation.

Simultaneously designing and simulating design variations gives a new idea for an engineer. Thus give an opportunity for innovations.

Development cost for the product is decreased by reducing the cost of the prototype or by eliminating the prototypes.

(ref:http://www-ipe.uni-duisburg.de/Rechnereinsatz/lehre/pw_download/cad2_cae_promech_tut_toogood_2.pdf)

TESTING

All glazing material must undergo impact load and environmental test requirements and should be labelled by manufactures as per part 1201 - SAFETY STANDARD FOR ARCHITECTURAL GLAZING MATERIALS. The impact load being applied at a height of 1100mm to 1500mm above the playing surface, since the ball hits maximum on these heights.

Glass walls must satisfy the following conditions:

A glass wall in racquetball or squash court subjected to impact load shall remain undamaged following a test impact.

The deflection of the walls shall not be greater than 1.5 inches (38mm) at the point of impact.

(Ref: Oregon structural specialty code, 2007, chapter: glass and glazing)

Testing Equipment

The impact test frame is used to minimize the movement and deflection of the specimen during test. The testing equipment used for testing glass panels are shown below.

The test specimen will be placed in a frame and the four edges kept fixed. The frame is made up of wood. The inner subframe is used to secure the test specimen edges; the material used for inner subframe is neoprene strips, which shall be in contact with specimen corners. The pressure on the test specimen shall be controlled, and the compression of the neoprene strips shall be between 10 and 15 percent of the neoprene. To limit the compression of the neoprene and prevent distortion of the subframe, metal shims of an appropriate thickness shall be used.

Impact load is applied on the glass by impactor from the height of 48 inches. The impactor shall be a leather punching bag or a rubber bladder. The bag is filled by chilled lead shot of a weight of completed assembly of 100 pounds. After filling the leather bag, it is been tied with a cord or leather thong to a metal sleeve. The exterior of the bag shall be completely covered by ½ inch wide glass filament reinforced pressure sensitive tape.

Impact test procedure: Each specimen (glass panel) shall be struck within 2 inches of its geometric center with the impactor dropped from a single height. Specimen is impacted one time from drop height of 48 inches. If the specimen withstands this impact will pass the quality and reaches the customer.

It is very important for the manufacturer to perform the impact test on the glass panel, since it rules from the federation. The manufacturer has to label the following details on the glass panels, like manufactured date, test passed, and test conducted date. The tempered glass is permanently labelled to indicate it conforms to ANSI Z97.1-1972 or 1975 or is accompanied by a certificate certifying conformance to ANSI Z97.1-1972 or 1975.

(ref: part 1201 - SAFETY STANDARD FOR ARCHITECTURAL GLAZING MATERIALS)

IMPACT TESTING WITH PRO /MECHANICA

Pro/Mechanica is a multi discipline computer aided engineering tool that enables the user to simulate the physical behaviour of a model, and therefore enable the user to improve the design. Pro/Mechanica can be used to predict how a design will behave in the real world by calculating stresses, deflections, frequencies, heat transfer paths etc.

Pro/Mechanic is the most effective analysis tool for testing the impact loads on the glass panels. The above mentioned test procedure is takes long time and prototype required for analysis. Pro/mechanic gives the accurate results for applied loads on the specimen and different sets of load could be applied without redesigning the specimen. The Mechanica packages include thermal, motion simulation and structural analysis. Analysis is the larger set of pull down menus and dialog boxes within CAD packages. Pro/Mechanic is integrated and run simultaneously with the 3Dsolid modelling computer package Pro/Engineer. After a design is modelled, the user may select Pro/Mechanic option to access finite element analysis.

There are two types of model for