Large Increment Method For Plate And Parallel Computation

Large Increment Method(LIM)involved by the present dissertation is a novel force-based method based on the generalized inverse matrix theory for solving solid material nonlinear problems in small deformation and small displacement conditions.Compared with the traditional displacement-based Finite Element Method(FEM),the advantages of LIM are high stress calculation precision and less computational time consumption,especially it is suitable to spatial and time parallel computation.For the spatial parallel computation,LIM can parallelly compute the constitutive equations of each element.For the time parallel computation,LIM is endowed with the advantage of the computation in time domain in the following way,at each moment the linear elastic results are used as the initial value,the material nonlinear properties during different loading history can be introduced parallelly and the iteration procedure covering the whole loading path can be done by the global deformation compatibility condition.The displacement-based Reissner-Mindlin plate elements for analyzing moderately thick plate problems are also commonly suffered from shear locking in the analysis of the thin plate problems.Since in this theory,as the thickness span ratio of the plate decreases gradually,the shear strain energy is much greater than the bending strain energy,the bending deformation is much less than the actual deformation,and it also causes so-called shear locking phenomenon.The root of the shear locking is a numerical problem due to the three-dimensional plate problem is simplified to a two-dimensional problem under too strong assumptions.The LIM is a force-based FEM with the force unknown,which has some prominent advantages to solve it.In the present dissertation,the force-based 4-nodes and 8-nodes quadrilateral plate elements are proposed innovatively by assuming the appropriate generalized inner force fields for solving plate bending problems using LIM.The governing equations of the proposed plate elements are obtained by introducing the principle of complementary virtual work with the equilibrious element generalized inner force fields and the simplified moderately thick plate displacement fields.Due to the assuming generalized inner force fields can comparative accurately reflect the inner force distribution for the thin plate and moderately thick plate,therefore the proposed plate elements are not easily appear shear locking phenomenon when the thin plate problems are solved by LIM.Based on the elemental governing equations and the generalized inverse matrix theory,the necessary and sufficient conditions for determination of the zero energy modes(ZEM)and ill condition for the element flexibility matrix are presented.The results are compared with the exact solutions and the solutions from displacement-based FEM,the good convergence and accuracy of the proposed plate elements using LIM for analysing the moderately thick plate and thin plate problems are verified.In order to make LIM more practical for solving the plate elastoplastic problems,the consistent elastoplastic flexibility matrix formula of the proposed plate element is provided in the dissertation.The numerical examples show that the applicability and high computational efficiency of LIM is proved for solving the elastoplastic problems.In the dissertation,the parallel environment is easily to be reached for users.They are: the hardware environment is 16 GB memory,8 cores and Intel(R)Core(TM)CPU small workstation,the software environment is the 64-bit Windows 7 operating system and the programming environment based on Open Multi-Processing(OpenMP)and Message Passing Interface(MPI).OpenMP is a standard for shared memory parallel programming and is applicable to the shared memory of multi-core computer.MPI is a kind of standardized message passing programming model,which is applicable to the shared memory of multi-core computer and distributed memory computer.The OpenMP is used for the parallel computation in spatial domain,and MPI is used for the parallel computation in time domain.Through the analysis,it shows that LIM has an excellent parallel efficiency in both space and time parallel computation.