Research On Computational Theory Of Finite Particle Method For Fine Analysis Of Structures

The computation theory of spatial structures has experienced a process from simplified methods based on continuum theory (such as plate analogy method and shell analogy method) to the finite element method. But macro method is still the mainstream of structural analysis, and the overall mechanical behavior is focused. The macro method models structures using link elements or beam elements, and key joints using solid elements. This approach basically satisfies the needs of design, but the size effect of sections is neglected. Meanwhile, complex joints cannot be analyzed concurrently, and the real bearing capacity and the failure mechanism of structures cannot be obtained. In order to solve this problem, fine analysis is quite necessary, which is the hot spots at home and abroad in the recent years. This dissertation models structures using a new numerical method-finite particle method (FPM), and establishes a computation theory for fine analysis of large-span spatial structures.This dissertation has described the research status quo of the fine analysis. The advantages and disadvantages of macro models, multi-scale models and fine models are summarized. The accuracy and stability of main kinds of numerical methods are summed up. The research on the development, application and characteristics of FPM is carried on, and then the advantages and key problems of using FPM to do fine analysis are presented. The importance of the research on fine analysis theory based on FPM is emphasized.The basic principles of FPM are briefly introduced. Some primary concepts, for example, point description, path unit description, the mechanism for describing deformation of continua, governing equations, etc., are given. The general computation framework is presented. The calculation formulas for internal force of each kind of element used in the analysis of spatial structures are derived, including the beam element for macro analysis and the shell element and the solid element for fine analysis. In this way, this dissertation has the basic analysis tools.The parallel acceleration of FPM is researched using the advantage of parallel characteristics. The solution of governing equations of particles and the computation of internal forces of elements is independent. This dissertation studies the parallel acceleration of FPM on GPU(Graphics Processing Unit) from data storage, thread mapping, particle force assembly, multithread saving, program optimizing and other aspects. The computations of beam elements, shell elements and solid elements are speed up tens of times, providing reliable technical supports for structural fine analysis using FPM.The method for simulation of contact and friction behaviors in fine analysis based on FPM is put forward. This dissertation establishes a spatial cell data structure to store the boundary particles, and narrows the range of searching particle-face pairs in global. The contact status of each pair is determined using inside-outside method, and if contact accurs, the defense node method is then used to satisfy the contact constraint condition, thus the accurate contact force and friction force can be calculated. This method is implemented in parallel on GPU to achieve high efficiency. Numerical examples demonstrate that this method has sufficient accuracy and stability in simulation of impact, sliding friction and static friction behaviors using shell elements or solid elements.The connection method based on FPM is proposed to implement multi-scale analysis of structures. In FPM, particles are the basic units and explicit integration is adopted. The multi-scale modeling method proposed in this paper is based on these FPM’s characteristics and the plane section assumption of beam and shell elements. The particles in the connection section are divided into master and slave particles. The mass, mass inertia matrix, force and moment of slave particles are assembled into master particles. After the motion equations of master particles are solved, slave particles’ displacements are acquired from displacement constraint conditions, thus the connection of elements with different dimensions is implemented. The results of numerical examples demonstrate that this multi-scale modeling method is effective for beam-shell, beam-solid and shell-solid connections and achieves good accuracy and stability in geometric nonlinear and dynamic problems.The intelligent particle distribution method based on FPM is proposed, which implement the balance of efficiency and accuracy in fully fine analysis. Using stress smoothing and Zienkiewicz-Zhu posteriori, the error estimator is given, which can determine and track the yield regions and other damage positions automatically. Father element is splitted into four sub elements to implement fission in damage positions. Through transfering physical quantities from old particles and elements to new ones, the states can retain consistence. Numerical examples dealing with high nonlinear problems such as buckling and impact demonstrate the robustness of the algorithm.The whole procedure and behaviors of fine models of typical plate-like spatial trusses with welded balls are researched with FPM. The static displacement response and the real stress distribution of fine models are abtained, accelerated by loading slowly and setting fake damping. The local failure and bearing capacity of the fine model is obtained. The dynamic response under earthquake is researched, and the whole procedure is tracked. This example indicates that the fine analysis can obtain the real behaviors and bearing capacity while the macro analysis cannot.The fine analysis of structures computer-aided design system (FASCAD) is developed which is based on the fine analysis computational theory using FPM, and integrates the pre-process, the post-process and numerical analysis modules. This system includes contact analysis, multi-scale analysis, intelligent particle distribution and other kernel modules. The fine model display, result display, data exchange and other functions are implemented.Theoretical derivation and numerical examples demonstrate that the computational theory for fine analysis presented here is correct, and the algorithm is effective and general. The computational theory can be the base of structural fine analysis and behavior research. The conclusions and problems that should be studied further are summarized at the end of dissertation.