Actas JP2011 - Universidad de La Laguna

Actas XXII Jornadas de Paralelismo (JP2011) , La Laguna, Tenerife, 7-9 septiembre 2011B. Improvements on BEMAPEC functionalityUsing the previous version of BEMAPEC [12] wehave developed several improvements. First, we definethe type of problem and the geometry of solidsthat are involved. Then we mesh these solids anddefine boundary conditions and type of contact. Afterthat, BEMAPEC calculates coefficients for eachmeshed element. We build the equation system fromthose coefficients. Finally, the equation system issolved and the whole problem is computed by meansof an iterative process. This last stage, equation systemdefinition and problem resolution, is the functionalityadded to the program.The resolution process comprises the followingsteps:1. Assembly of matrixes equation system Ax=B:the coefficients computed by the integration of eachelement over all the rest, are used to do the assemblyof the A matrix and the B vector for the equation systemAx=B. A and B elements are determined takingin account the solid and the region that each elementbelongs to (contact zone or free zone).2. Resolution of equation system by GaussMethod: to solve the previously obtained equationsystem, it is necessary to use Gauss Method withpivot. This choice is due to effectiveness and efficiencyreasons, so as the intrinsic characteristics ofthe problem that generates a large amount of zerosin A and B.3. Resolution of thermal problem (if it is necessary):this step is considered just for thermal orthermoelastic problems. The process starts with theresolution of the equation system by using the GaussMethod. So we obtain an X vector that is employedto establish boundary conditions in the contact zonefor each element that belongs to the contact surfacesof each solid. This process finishes with the writingof temperature and heat flow parameters related toeach thermal element into a file.4. Resolution of elastic problem (if it is necessary):this stage is carried out for elastic or thermoelasticproblems. First we solve the equation system byGauss Method and the resulting X vector allows usto determine the elastic conditions for each elementof either contact or free zones. Once each element ofboth solids has its boundary condition, relative displacementscan be calculated. Next, every value foreach element of both solids is written in an outputfile. We need now to check the obtained partial results.Firstly, tension checking is made to determinewhich elements are leaving the contact zone. Whenthere are no elements coming into or out from thecontact zone, we write in an output file the new elasticcondition values for every element and the thermalresistance values for those elements that belongto the contact zone.5. Resolution of thermoelastic problem (if it isnecessary): this stage is considered for thermoelasticproblems. In that case, firstly the thermal problemis solved. Then, it is solved the elastic problem.Subsequently, only in the case that contact betweensolids is imperfect, a comparison among thermal resistancesfor those elements that belong to the contactzone is made. If the result of such comparisonis higher than a certain tolerance, thermal resistancevalues will be modified, and process will be repeatedagain.6. Resolution of iterative process (if it is necessary):it could happen, when elastic or thermoelasticproblems are being solved, that some specific conditionscan appear that makes come back to point 1of the resolution, and process would have to be executedagain. Conditions that make the process startsa new iteration depend on the type of problem thatis being solved. So, it is necessary to do the followingdistinction:• Elastic problem: once equation system is solved,results need to be checked. In this case, firstly,tension checking for every element that belongsto the contact zone is carried out. This allows usto determine which elements come out from thecontact zone. Once tension checking is done,if the number of elements that come out fromthe contact zone is zero, interpenetrations arechecked. Interpenetration checking determineswhich elements come into the contact zone.After tension checking is finished, if there is anyelement coming out from the contact zone, theprocess will be repeated. If no-one elementscome out from the contact zone but some elementscome into such zone, the process also willbe repeated.• Thermal problem: in case of thermoelastic problems,process can be repeated because of severalreasons. A reason is the previously explainedone for the elastic problem. Another one is dueto the thermal problem. In that case, the comparisonbetween thermal resistances is carriedout. If the result of this comparison differs fromany tolerance in amount higher than a certainvalue for any element that belongs to the contactzone, the problem will be solved again withthose new resistance values.In short, process will stop when no-one elementcomes into or out from the contact zone (elasticproblem) and thermal resistance differs in an amountlower than a certain value (thermal problem) for everyelement that belongs to the contact zone.IV. Experiments and ResultsWe have carried out several experiments to comparethe execution time for FORTRAN’s applicationversion [8] and BEMAPEC application.A. Thermal problemsProof cases used in the thermal problem are basedon two solids in contact (Fig. 1). Both solids arecubes made up by 640 elements. 128 elements fromeach cube belong to the contact zone. The type ofcontact between solids is perfect, the environmentis vacuum. For those nodes on the potential con-JP2011-149