The Extended Application Of Parallel Computing-based Large Increment Method In Computational Solid Mechanics

General Inverse Force Method is an iteration procedure covering whole loading path. Itsincrement steps are determined by the changes of loading statement. Unlike the traditionalFinite Element Method, the size of its each increment step is not restricted to assure precision,thus it is often called Large Increment Method (LIM). As a finite element algorithm, LIM wasborn with the capacity for numerical parallel computation and the parallel computation inspatial domain. Better still, it can parallely solve the constitutive equations of each elementwithout dividing a structure into several substructures. Moreover, LIM was endowed with theadvantage of the parallel computation also in time domain, which is not provided by any otherfinite element algorithms. In the case that the loading path is complicated, the parallelcomputing in time domain ensures the potential of greatly accelerating computation speed. Inthe first part of the present dissertation, the parallel computation in time domain washighlighted; the deficiencies and difficulties of the preliminary research of the parallelizationfor LIM were pointed out; and two parallel Scheduling Schema including numerical parallelcomputation as well as parallel computations in spatial and time domain were provided. As isknown to all, parallel computing was proposed to deal with the large scale computations. Thelager the scale is, the higher the computational efficiency could be. However, before thispaper, LIM had no capability to cope with the analysis of complex solid structure whichrequires large scale computation, because of the insufficiency of element types. Therefore, themost important and prerequisite thing is to construct an element library for LIM, and make itrich. Only when LIM can cope with the large scale computational problems and provideprecise computational results, the parallelization of LIM can be implemented efficiently, andthe power of parallel computation for LIM can be shown.In this dissertation, the key work was the extended application of LIM in computationalsolid mechanics. Detailedly speaking, the key work was to develop2D and3D solid elements,and then to construct a finite element library for LIM. First of all,3D frame element wasabsorbed into the element library and coded for LIM program. The computing features ofLIM were emphasized based on the discussion of the numerical computation using frame element. To enrich the finite element library, two methods for developing2D and3D solidelements were proposed creatively. Accordingly, two types of elements were proposed, onewas named ’nodal force type’ element and the other was named ’stress type’ element.Nodal force type element was named by the reason that parts of the elemental nodalforces were employed as the elemental generalized inner forces. Generally speaking, theelemental generalized inner forces were composed of the fewest independent unknown forceswhich are sufficient to determine the stress distribution within an element, and the unknownforces could be chosen arbitrarily. Therefore, in consideration of all kinds of2D and3Delements, the special elemental basic statically determinate system was chosen, the localcoordinates of this system was defined. Hence, the basic force system was chosen, and theappropriate elemental generalized inner forces were determined. Under the clearly definedbasic system, the general forms of the elemental governing equations were proposed byconsidering coordinates transformation and equilibrium relationship. Because that the shapeof element and the number of nodes were not limited in the general forms of the elementalgoverning equations, one can obtain any2D or3D solid element with a given number ofnodes by implementing the proposed general forms. It should be noted that the general formsof the elemental governing equations can be easily realized by programming because of itsstrong systematicness. In the present dissertation, four2D elements and two3D elementswere developed for the element library of LIM, and the codes of the proposed general formsand elements were accomplished. Some illustrative numerical examples were solved using theproposed library. The results were compared with those obtained from displacement-basedfinite element method and analytical close-form solutions, which has clearly shown thecomputational convergence rate and accuracy of LIM. Furthermore, the insensitiveness to themesh distortion, coordinates as well as the sequence of mesh node labels was also observed.The governing equations of stress type element were obtained by introducing principle ofvirtual work. With in an element, the approximations of stress field and displacement fieldwere presented as interpolation polynomials, respectively. Because that the linear independentcoefficients of the assumed interpolation polynomials of stress field were employed aselemental generalized inner forces, the elements were named stress type elements. In thepresent dissertation, the polynomial of each stress component was deduced from the assumed stress function firstly, and then the elemental governing equations were obtained,consequently the stress type elements were developed. Based on the elemental governingequations, the necessary and sufficient condition for determination of spurious zero energymodes is presented, and the spurious zero energy modes as well as the ill conditionedflexibility matrix were detected to avoid numerical error. To suppress spurious zero energymodes, another method named iso-function method which was based on basic displacementmodes was employed. By using which, one hexahedral element with the absence of spuriouszero energy modes was developed. In two manners described above, six2D elements andthree3D elements were developed for the element library, and the codes of the proposedelements were completed. The illustrative numerical examples were also solved using theproposed stress type library and the computational convergence rate and accuracy of LIM wasshown.To make LIM more practical in solving material nonlinearity problem, the consistentelastoplastic matrix for elemental stage is provided in the last part of the present dissertation.By the numerical example, the applicability of LIM was proved, and the potential of parallelcomputation was imply.In summary, the solid element library which including ten2D elements and five3Delements was proposed for LIM modeling arbitrary configurations. Because of theextensibility of the proposed manners for obtaining elements, following the methods, userscan develop their own elements as needed. Benefit from the achievements of the presentdissertation, the application of LIM in computational solid mechanics has made a remarkableprogress. Meanwhile, the object oriented serial program of LIM has been completed in themain, based upon which, the optimization and parallelization of the program can be done inthe future.