Stress-Type Time-Domain Artificial Boundary Condition For Finite-Element Simulation Of Near-Field Wave Motion And Its Engineering Application

The scale of the major construction projects (such as high arch dam, nuclearstation, high-rise building, long-span bridge and so on) in our country has leaped intothe front ranks of the world. The time-domain numerical simulation of the majorconstructions under the seismic or blast load is an effective method for their designand safety evaluation. The analysis models of the major constructions requireconsidering the energy radiation of infinite foundation, forming the near-field wavemotion problem or called dynamic soil-structure interaction problem. The commonnumerical method to analyze the near-field wave motion problem is as follows. Afictitious boundary usually called artificial boundary is introduced to partition thewhole opening system into two parts, i.e. near-field finite domain and far-field infinitedomain. The former includes structure, and inhomogeneity and nonlinearity of media,which can be modeled by finite element method. On the other hand, the latter issimplified as linear elastic media, and satisfies the radiation condition at the artificialboundary. In practical computation, the far-field infinite domain is truncated. Aboundary condition is imposed on the artificial boundary to model the energyradiation effect of the truncated infinite domain, which is called artificial boundarycondition (ABC) or nonreflecting, transmitting, absorbing, radiation boundarycondition. Actually, the artificial boundary problems are ubiquitous in many fields ofphysics and engineering, such as acoustics, electromagnetics, computational fluiddynamics, meteorology and so on, which belonging a new interdisciplinarynumerically computational science subject. An effective ABC should combine withfinite element method to form a stable, accurate, efficient and easily implementednear-field wave motion analysis method. At present, many ABCs have been proposedbased on the different mathematical, physical and mechanical methods. However,there is still no consensus on the optimal ABC.This dissertation studies the stress-type exact time-domain ABC and itsengineering application. First, the time-domain method can consider theinhomogeneity and nonlinearity in the near-field finite domain. Second, thestress-type ABC indicates that the ABC is an expression of interaction stress betweenthe near-field finite domain and the far-field infinite domain. It can compatible withthe finite element method very well as a natural stress boundary condition, leading tothe numerically stable near-field wave motion method. Last, with the computer leveland engineering accuracy requirement improving, the exact method should be a trend.Although the exact method has lower efficiency than the approximate method, it canbe placed nearer source or structure than the latter, leading to the lower computational cost in the near-field finite domain.The problem statement of the far-field infinite domain is first solved by theseparation of variables. The temporal global ABC is obtained, where the response at aconstant is related with the current and all before constants. To decrease thecomputational cost, the convolution kernel compression technique, combining therational approximation and high-order spring-dashpot-mass model, is then applied tolocalize the obtained ABC. A stable, accurate, efficient and easily implemented ABCis finally obtained. In this dissertation, the far-field infinite domains include thewaveguide and exterior models of out-of-plane wave motion problem and theone-dimensional elastic wave radiation model. The ABC from the former can exactlymodel the out-of-plane wave motion problem, but many works still need to be furtherstudied for the application to the major construction. On the other hand, the ABC fromthe latter can be directly applied to engineering practice to approximately model theradiation of the general non-symmetric elastic waves in the exterior model. Theconcrete works in this dissertation are as follows.1. The convolution kernel compression to localize the convolution transformbetween force and displacement.(1) The necessary and sufficient stability condition for the rational approximationof frequency response function of infinite domain is presented based on the stabilitytheory of linear system. A parameter identification method guaranteeing stability apriori by enforcing the stability constraint condition is further developed based on thepenalty function method and the genetic-simplex optimization algorithm. Theresonance phenomenon in a stable system is also discussed, and a method avoidingresonance is proposed.(2) Three new high-order spring-dashpot-mass models are proposed, as therealizations of the rational approximation into the time domain. Thecontinued-fraction expansion of rational function is developed to calculate the modelparameters. A seismic input method for the high-order spring-dashpot-mass models isalso presented.(3) The effectiveness of the modified convolution kernel compression techniqueis demonstrated by analyzing several typical foundation vibration problems.2. Stress-type exact time-domain ABC for out-of-plane wave motionproblem.(1) The modal function of artificial boundary is first chosen according to thephysical boundary conditions of the waveguide and exterior models. The Fourierseries expansion is then applied to represent the spatial globality.(2) The modified convolution kernel compression technique is applied to themodal frequency response functions to localize the exact ABC, leading to a symmetricsystem of second-order ordinary differential equations of the auxiliary variables intime. (3) Based on the spatial and temporal treatments mentioned above, thefinite-element formulas of exact ABC are developed. They can assemble directly andcouple seamless with the finite-element model of the near-field finite domain.3. Stress-type time-domain ABC based on radiation of one-dimensionalelastic waves and its engineering application.(1) Based on the modified convolution kernel compression technique, the exacttime-domain ABC is developed to model the radiation of cylindrical and sphericalelastic waves from the near-field finite domain into the far-field infinite domain. Theviscous-spring boundary is the low-order form of this ABC.(2) The viscous-spring boundary is further improved. The two-dimensionalin-plane tangential boundary and the three-dimensional tangential boundary aredeveloped.(3) The simplified input methods of the plane seismic waves of inclined andvertical incidence are proposed for the viscous-spring boundary. The seismicresponses of Xiaowan arch dam are calculated and compared with the results by usingthe multi-transmitting formula. The effect of material nonlinearity of concrete is alsoconsidered simply.4. Other research works.(1) The time-domain recursive evaluation based on the rational approximation isdiscussed. The bilinear transform is used to obtain the discrete-time rationalapproximation from the continuous-time one. The single-step time-domain recursiveformulas are constructed by applying the state space transform.(2) The cutoff frequency and dispersive property of wave propagation in thesemi-infinite rod on an elastic foundation and in the waveguide model are studied. Aconclusion that the local ABC based on the one-dimensional outgoing wave can notsolve such problems satisfactorily is drawn, which is demonstrated by numericalexperiments.(3) The lumped-mass finite-element equations for out-of-plane wave motion arepresented in Cartesian and polar coordinates, respectively. The element matrices ofthe normal finite elements are also derived. The periodic property, cutoff frequencyand dispersive property of the wave propagation in the one- and two-dimensionalfinite-element mesh of spatially and temporally uniform discretization are discussed.