The P-version Adaptive Finite Element Methods And Fast Solving Algorithms For 3D Concrete Aggregate Models

As a complicated 3D weak discontinuity problem with randomly distributed particles in different shapes,numerical simulation of concrete aggregate models(CAMs)usually requires high accuracy for the computational results on the interface of the coarse aggregates,but a sharp increase of the computer's physical memory usage will be caused by the traditional finite element methods(FEM),such as refine the meshes throughout the domain.However,most of the researches have focused on the realization of approximate realistic CAMs and the optimal scheme for particle generation,after which the relevant numerical simulation experiments were carried out to investigate corresponding mechanics property of concrete,and there have been scarce studies investigating the corresponding computational efficiency and accuracy with respect to such large-scale finite element problems.Therefore,developing an efficient numerical analysis method for solving such problems is necessary.In this work,we design the p-FEM to solve 3D CAMs problem and study the corresponding fast algorithm,the main work and conclusions are as follows:1.In this paper,a hybrid realization method was proposed in order to rapidly obtain the concrete aggregate models with high volume fraction of spherical particles by combining Fortran and ANSYS softwares.And the corresponding ellipsoid aggregate(pebble)model,the convex polyhedral aggregate(gravel)model and the mixed model with different shape aggregates were also generated.The results of several examples showed that the relevant data of three-graded concrete model with spherical aggregate particles can be fastly obtained and the corresponding aggregate content can reach about65%.The hybrid realization method can easily separate the aggregate particles from the interface layers and thus the complex element attribute discrimination can be avoided in the finite element mesh.Finally,the validity of the proposed hybrid method was further verified by finite element numerical simulation for the ellipsoidal aggregate model and the convex polyhedral aggregate model.2.A p-version FEM(p-FEM)combining higher-order elements with the adaptive method is proposed in this work to solve 3D CAMs problems,and associated adaptive computational program and post processor program are composed.Aiming at two typical3 D inclusion problems,discussions focused on the influence of different convergence criterions on the computational results of each point on the interface are made to verifythe effectiveness of the p-FEM,after which the p-FEM is successfully applied to the numerical simulation of CAMs.In order to establish finite element models of the concrete,an efficient hybrid realization method(HRM)which combines the mature finite element analysis softwares ANSYS and Hypermesh is also presented in this paper.The numerical results show that the proposed p-FEM can efficiently solve the concrete-like particle-reinforced composite problems,and more accurate numerical results could be achieved with fewer elements,even those of poor quality.And in process of CAMs establishment,complicated mathematical calculation of the element attribute discrimination can be avoided and consistency of elements between different materials can be easily achieved with HRM.3.Aiming at the 3D concrete aggregate model discretized with high order elements,the corresponding fast solving algorithm is designed for such large scale finite element system.The two-level method and the multilevel method are designed to solve the tetrahedral hierarchical equation of high order.Essentially,these methods are to naturalize the solving process of equation of high order into the linear equations.The utilization of hierarchical basis can avoid the establishment of algebraic criterion of the congruent relationship for the index of unknown variable and the subordinate geometrical nodal type,thus the formulation of mesh transformation operator becomes easier and the corresponding calculation efficiency is improved.The numerical tests for several typical3 D CAMs have verified the effectiveness of the resulting method.This provides a fast computational method for 3D CAMs.