A spatial hashing method was introduced to accelerate the contact detection process in the numerical manifold method. All objects (blocks) in the work space are hashed to a one dimensional hash table ...based on a spatial grid, then only blocks within the same place in the hash table need to do contact detection. The proposed method has a time complexity of O(n). Experiments show that the spatial hashing contact detection has a significant improvement in performance.
Summary
Numerical Manifold Method (NMM) is an extension of Discontinuous Deformation Analysis which contains and combines FEM and joint/block oriented DDA in a unified form. At present, application ...of NMM is mainly limited to two-dimensional analysis which is not realistic for many underground excavation works. In the present paper, three-dimensional NMM based on tetrahedron and hexahedron elements is proposed. The corresponding three-dimensional cover contact detection algorithms which have some fundamental properties different from the corresponding two-dimensional analysis are also developed. Based on the present formulations, engineering problems with arbitrarily oriented discontinuities can be modeled and realistic modeling of construction works becomes possible.
Based on Numerical Manifold Method (NMM), a novel method is presented for computing Stress Intensity Factor (SIF) of cracks. The Williams expansions are employed as the analytical solutions in the ...mesh containing the crack tip. And high-order polynomial functions are used as the numerical solutions in the surrounding meshes. Then the SIFs are computed via combination of the numerical solutions and the analytical solutions. Meanwhile, the meshes in NMM need not conform to the physical boundaries including the crack edges, allowing the cracks arbitrarily align within the meshes. The given example shows the validity of the method.
Due to the independence of physical domain and the mathematical cover system, the numerical manifold method (NMM) can efficiently simulate crack propagation without remeshing. At the same time, the ...polygonal elements are also very attractive due to their great flexibility in meshing and high efficiency in materials modeling. In the present paper, the NMM is applied to solve 2-D crack propagation problems on polygonal elements. Our numerical results show that the proposed method can well capture the crack growth trajectory compared with the reference solution
The numerical manifold method (NMM) is a representative among different numerical methods for crack problems. Due to the independence of physical domain and the mathematical cover system, totally ...regular mathematical elements can be used in the NMM. In the present paper, the NMM is applied to solve 2-D linear elastic crack problems, together with the comparison study on the accuracy of n-sided regular mathematical elements, i.e., the triangular elements (n=3), the quadrilateral elements (n=4) and the hexagonal elements (n=6). Our numerical results show that among different elements, the regular hexagonal element is the best and the quadrilateral element is better than the triangular one.
Numerical Manifold Method (NMM) with partially overlapping covers is a new method based on independent covers analysis, which is limited to two-dimension problems currently. Analysis of high - low ...mixed order 3D NMM with partially overlapping covers is carried out via construction of partially overlapping system based on hexahedron mesh and by using freedom constraint between nodes, so the corresponding element matrix formula is given and numerical examples shows the validity of the method. The results show that computation degree of freedom is greatly reduced when the accuracy requirement is satisfied. In some concerned independent cover areas such as dam heel, the improvement of calculation accuracy caused by the upgrading of independent cover function or encrypted cover is obvious, and has little impact on the calculation results in the surrounding cover.
Numerical simulations of longitudinal wave propagation in a rock bar with microcracks are conducted by using the numerical manifold method which has great advantages in the simulation of ...discontinuities. Firstly, validation of the numerical manifold method is carried out by simulations of a longitudinal stress wave propagating through intact and cracked rock bars. The behavior of the stress wave traveling in a one-dimensional rock bar with randomly distributed microcracks is subsequently studied. It is revealed that the highly defected rock bar has significant viscoelasticity to the stress wave propagation. Wave attenuation as well as time delay is affected by the length, quantity, specific stiffness of the distributed microcracks as well as the incident stress wave frequency. The storage and loss moduli of the defected rock are also affected by the microcrack properties; however, they are independent of incident stress wave frequency.
With high-order numerical manifold method (NMM) or high-order discontinuous deformation analysis method (DDA), computational accuracy of structure deformation can be improved greatly. However, poor ...accuracy is obtained and even computation is not convergent while treating large deformation problems, due to inaccurate or incorrect high-order initial stress formulae. Based on 2D triangular mathematical meshes and polynomial cover functions in high-order NMM, exact formulae for high-order initial stresses are deduced to depict configuration change of structures under large deformations. The formulae are expressed in polynomial forms so as to be used in simplex integrations. The approach is also extended to high-order DDA. Comparing with analytical solutions, accurate results for large deformation of a cantilever beam prove the validity of the proposed formulae.
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