六面体有限覆盖的三维数值流形方法的非线性分析

Nonlinear analysis of three-dimensional numerical manifold method with hexahedron finite covers

对三维问题的分析是数值流形方法发展的必然,在数值流形方法覆盖位移函数的基础上构造了一种六面体有限覆盖的三维流形单元,推导了相应的应变矩阵、刚度矩阵及平衡方程等表达式。同时,由于目前数值流形方法的模拟分析主要是采用线弹性模型,而对于非线性模型分析研究很少;根据数值流形方法的特点和岩土体的本构模型,给出了适用于数值流形方法进行非线性分析的算法。该方法利用中点增量法进行求解,以改变E-μ模型和K-G模型中弹性模量的方式来反映非线性,其实质是用分段线性来取代非线性。通过地基沉降计算算例表明,数值流形方法在三维岩土体中进行非线性分析中是有效的。

Analyzing three dimension is the developmental trend of numerical manifold method. Three-dimensional manifold element with hexahedral finite element covers is constructed by cover displacement function of numerical manifold method, strain matrix, stiffness matrix and equilibrium equations are derived. Simultaneity, linear elastic model is mostly adopted on numerical manifold method for problem analysising persently, but nonlinear model is researched very little, calculating formulations of numerical manifold method for nonlinear analysis based on the characters of numerical manifold method and constitutive models of rock and soil mass is presented. The elastic modulus of E-μ model and K-G model is altered to describe the nonlinear relationship by midpoint incremental method; in fact subsection linear ralationship is substituted for nonlinear ralationship. Finally, an example of foundation settlement calculation is given; the calculation result shows the validity of nonlinear analysis of three-dimensional numerical manifold method for rock and soil mass.