这丰富了数值流形方法的动力计算方法。
将增量流形方法推广到岩石大变形问题。
Incremental manifold method is extended to the large deformation for rock.
数值流形方法是目前岩石力学分析的主要方法之一。
The Numerical Manifold Method (NMM) is one of important numerical methods to model rock mechanics problems at present.
数值流形方法常基于有限元法三结点或四结点单元。
Usually the numerical manifold method (NMM) is based on meshes of three - or four-node element.
数值流形方法是目前岩土工程数值分析方法的一个研究热点。
The numerical manifold method is pop method of research for the numerical method in geotechnical engineering.
本文利用数值流形方法对一层状岩石边坡的倾倒破坏过程进行了模拟。
In this paper, numerical manifold method, a new numerical analysis method, is used to simulate the toppling failure process of a stratified rock slope.
与传统的数值流形方法相比，无网格流形方法的有限覆盖形状更加灵活。
Compared with the conventional numerical manifold method, the shapes of the finite covers can be selected more easily.
本文研究了如何从加权残数法出发建立拉普拉斯方程数值流形方法的求解方程。
So we should implement the method of weighted residuals to derive the governing equations of the NMM.
本文研究了如何从加权残数法出发建立拉普拉斯方程数值流形方法的求解方程。
The numerical manifold method of Laplace equation was presented, it was also more general than the minimum potential energy principle to obtain the governing equations of the NMM.
本文应用数值流形方法对静态断裂力学和动态断裂力学两个方面都进行了计算分析。
The method is numerically implemented and numerical analyses for a number of benchmark problems are made.
数值流形方法能够统一处理连续与非连续变形问题，有限覆盖技术是该方法的核心。
Numerical manifold method can solve both continuous and discontinuous deformation problems in a unified mathematical formulation. The finite cover is the essential technique in this method.
然后引入强度折减技术，结合数值流形方法提出了公路路基岩溶顶板稳定性的评价方法。
Then, the evaluating method of the stability of karst roof in roadbed had been established by combining with strength reduction technique and numerical manifold method.
同时，数值流形方法以覆盖技术为基础，为工程问题提供了一种更自然和简便的解决方法。
At the same time, the numerical manifold method is based on finite cover, it is a simple and convenient resolvent for engineering problem.
作者在流形方法里采用矩形作为数学覆盖，从另一角度提出了一种不同于有限元法的数值分析方法。
In contrast to the finite element method, another form of numerical method which is based on the using of rectangular math covers in manifold method is proposed.
根据数值流形方法的特点和岩土体的本构模型，给出了适用于非线性分析的数值流形方法的计算方法。
Based on the characteristics of the numerical manifold method and constitutive models of rock and soil mass, the formula of numerical manifold method for nonlinear analysis is presented.
本文用一个相当初等的方法，说明了如何把一个3维流形嵌入到5维空间中去。
Using an elementary method, we illustrate how a-3-manifold can be embedded into a 5-space in this note.
方法利用中心流形定理并结合平面系统的分支理论。
Methods Using the theorem of center manifold and bifurcation theory of planar system.
提出了一种基于相重构和主流形识别的非线性时间序列降噪方法。
A noise reduction method in nonlinear time series based on phase reconstruction and manifold learning was proposed.
利用中心流形约化方法证明了霍普夫分歧解的稳定性。
By using the method of centre manifold, the stability of the Hopf bifurcations is also proven.
应用作者所提出的数学模型和计算方法，对浮力射流形成后区的特性进行了预报。
The mathematical model and calculational method of buoyant jets given by authors are used to predict the characteristics of the zone of established flow.
提出了一个用流形元与有限元的变形和渗流非同步耦合的分析方法，用于模拟不连续块体在水压作用下的变形过程。
The calculation code including manifold method (MM) and finite element method (FEM) is developed to study the non-simultaneous coupling problem of stress-strain and seepage for discontinuous material.
分析了平衡流形展开模型的误差，给出了调度变量的确定方法。
The error of expansion model and the method of getting scheduling variable were proposed.
局部线性嵌入方法是一种应用广泛的流形学习方法，本文提出算法的一种改进，并将其应用于空间数据索引。
Locally linear embedding (LLE) is a widely-used manifold learning algorithm, in this paper we improve on the algorithm and put it to use in spatial data index.
通过本课程的学习，希望学生能初步掌握微分流形的基本概念、方法和技巧，学习从局部到整体的数学技巧。
This course should help students master definitions, basic peoperties and methods of differentiable and Riemannian manifolds, increase their ability from parts to a whole.
提出了一个非流形结构的表示方法——粘合边结构，其数学基础是代数拓扑中的复形理论。
An identification edge structure is put forward to represent non manifold modeling, which is built on the concepts and methods of the complex and CW complex in algebraic topology.
当应用于惯性流形多网格算法和非线性伽略金方法时，可证明类小波增量未知元方法的收敛性。
Convergence of the wavelet-like incremental unknowns method is proved when applied in the inertial manifold multigrid algorithms(IMG)or nonlinear Galerkin methods.
本文提出了用流形无法和子域奇异边界元法相结合模拟结构地震响应及地震破坏的方法。
In this paper, a method based on the combination of Manifold and Singular Boundary Element method to simulate seismic responses and failure processes of structures is presented.
这种方法以稳定流形理论为基础，通过设计合适的控制器将混沌系统引至目标轨道，使混沌得以控制和同步。
Based on the stable manifold theory, the chaotic system will be controlled and synchronized if it is guided to the desired target by designing a suitable controller.
本文第二章介绍了无穷维动力系统的惯性流形与近似惯性流形的约化思想，并讨论了KS方程的直接约化方法。
In this paper, the second chapter introduces the reducing idea of inertial manifolds and approximate inertial manifolds, and discuss the similarity reduction of KS equation.
利用不变形式的方法对复流形上的CR—子流形进行了一定的研究。
In this paper we study CR - submanifolds of a complex manifold using the method of the invariant form.
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