层合板及功能梯度板与多层和非均质地基相互作用的模型数值模拟

The application of plate based on the complex foundation is very broad. With the development of modern construction, it has put forward higher requirements. Plate based on foundation belongs to the category of interaction between plate and foundation, which is an important topic with theoretical significance and engineering significance. The traditional methods have some deficiencies in the analysis of this kind of problems. In addition, through literature analysis, it is found that the researches on the interaction between laminated plate and complex foundation are very rare, and there is a lack of in-depth understanding of the interaction mechanism between laminated plate and complex foundation. In this program, the numerical methods called scaled boundary finite element method (SBFEM) and precise integration method, which have higher accuracy and efficiency, have been applied to the interaction between laminated plate and complex foundation. The main works contain: The models for the analysis of mechanical properties of laminated plates and functionally graded plates have been established. The static and dynamic simulation analysis of the multi layered foundation (including the inclusion of complex geometries, voids, and uneven terrain) based on the scaled boundary finite element method is carried out, and a wide range of parameters are analyzed for the heterogeneous characteristics of layered soils. The static and dynamic characteristics of layered saturated/unsaturated soil are simulated by using the method of precise integration, and the influence of material parameters on the static and dynamic characteristics of the layered saturated soil is discussed. The models of scaled boundary finite element method for interaction between laminated plates as well as functionally graded plates and heterogeneous multi layered foundation have been established. Based on the precise integration method, a model for the interaction of laminated plates and functionally graded plates with layered saturated/unsaturated soils is derived. Therefore, the influence of materials of plate and foundation on the interaction between plate and foundation has been revealed. Based on the above research, this topic will provide a reliable theoretical basis and technical means for the design and application of laminated plates and functionally graded plates based on the foundation.

复杂地基上板的应用非常广泛，随着现代工程建设的发展，对地基板的分析计算提出了更高要求，地基上板属于基础与介质相互作用范畴，是具有理论意义和工程意义的重要课题。然而，层合板与复杂地基相互作用机理目前缺乏深入认识。本课题采用高精度和高效率的比例边界有限元方法和精细积分方法对该问题进行深入研究，具体为：建立考虑热荷载及非线性因素下的层合板及功能梯度板力学特性分析模型；开展基于比例边界有限元含非均质多层地基的静动力仿真分析，采用精细积分方法开展成层饱和/非饱和土静动力特性分析，探讨材料参数对成层及非均质地基静动力特性影响规律；提出基于比例边界有限元法的层合板及功能梯度板与非均质多层地基相互作用的求解模型；基于精细积分方法，得出层合板及功能梯度板与成层饱和/非饱和土地基相互作用求解模型，揭示板及地基参数对板与地基相互作用影响机制。通过以上研究为板在复杂地基工程应用设计提供可靠的理论依据和技术手段。

复杂地基上板的应用非常广泛，随着现代工程建设的发展，对地基板的分析计算提出了更高要求，地基上板属于基础与介质相互作用范畴，是具有理论意义和工程意义的重要课题。然而，层合板与复杂地基相互作用机理目前缺乏深入认识。本课题采用高精度和高效率的比例边界有限元方法和精细积分方法对该问题进行深入研究，具体为：基于比例边界有限元法建立了弹性板和层合板变形、应力及自由振动的高效分析模型；开展了基于等几何比例边界有限元方法的板和层合板力学特性分析；开展了功能梯度板（含压电）和功能梯度夹层板结构的静动力响应和屈曲的理论分析；构建了板结构热传导问题的比例边界有限元方法精细模型；深入开展了复杂地基刚度的比例边界有限元数值模型研究；提出了板与复杂地基相互作用的高效比例边界有限元及精细积分数值算法。本项目进一步建立了基于等几何技术的液体晃动高效数值计算模型；提出了基于等几何比例边界有限元和边界元方法求解热传导和热应力问题的高效数值模型；开展了层合梁、功能梯度梁和功能梯度夹层梁结构的静动力响应和屈曲分析；提出了压电和磁电弹智能柱壳（含层合壳）结构的静动力响应的高效SBFEM求解方法。通过以上研究为板在复杂地基工程应用设计提供可靠理论依据和技术手段。