Three-dimensional Numerical Manifold Method Research Articles

Low speed impact simulation of explosive charge based on three-dimensional numerical manifold method

The present work addresses the challenge of evaluating the low speed impact response of polymer bonded explosive charges with three-dimensional numerical manifold method. Based on the cover-based contact theory, the contact algorithm is implemented by transforming position relationships between reference points a0 and entrance block E(A, B). Meanwhile, based on statistical micro-cracks, a Visco Scram mechanical model for the explosive charge is established. Using the classic Steven test, the influence of charge thickness, diameter, and warhead shape on the mechanical response are analyzed under low speed impact. The simulation results indicate that, increasing the thickness of the charge can effectively avoid internal damage of the explosive caused by projectile extrusion and holder confinement; Increasing the aspect ratio of the charge can alleviate the large deformation; Increasing the shape and size of the warhead can make the charge extrusion shallower, alleviating the concave shear damage of the charge. The simulation results verifies that the developed contact algorithm in this paper can effectively solve 3D impact problems, and provides guidance in the design of charge structures to some extent in the weapon system.

A stable one-point quadrature rule for three-dimensional numerical manifold method

A stable one-point quadrature rule for three-dimensional numerical manifold method

Three-dimensional numerical manifold method for heat conduction problems with a simplex integral on the boundary

Three-dimensional numerical manifold method for heat conduction problems with a simplex integral on the boundary

Development of three-dimensional numerical manifold method with cover-based contact theory

Numerical manifold method (NMM) is a typical continuous-discontinuous coupling method. It unifies the continuous and discontinuous theories in the same program framework. In the present work, based on the cover-based contact theory, the specific solution of contact covers under five different positional relationships is given in detail, and the contact judgement conditions and contact cover solution formulas under each positional relationship are proposed. By converting the contact into the relationship between reference point a0 and the outer boundary of entrance block E (A, B), the contact algorithm between 3D blocks is implemented and programmed. The developed code is initially calibrated by two simple models, and its correctness is quantitatively verified by the motion of the inclined sliding model. Finally, it is applied to more complex structural deformation and dynamic collision problems. The 3D-NMM developed in the present work can be used for structural kinematics, structural deformation and dynamic collision problems, and has broad application prospects in the field of structural mechanics.

Enrichment of three-dimensional numerical manifold method with cover-based contact theory for static and dynamic mechanical response analysis

Based on the mathematical grid of 4-node tetrahedral finite element form, the dual cover system, weight function and displacement function of three-dimensional numerical manifold method (3D-NMM) are proposed. The derivation process of element stiffness matrix, inertial force matrix, loading point matrix, etc. are systematically demonstrated in the present work. Based on the cover-based contact theory, the contact detection algorithm among discrete 3D blocks is realized, and the 3D manifold framework is programmed. The accuracy of the developed code is firstly calibrated through two continuum deformation analysis: cantilever beam bending model and axial tensile model of thin plate with circular hole. Then it is applied to three complex discontinuous instability simulation (SHPB, brick wall structure and cliff slope) to verify the effectiveness and accuracy of the proposed contact algorithm. The classic Steven low velocity impact process is also simulated, and the deformation and failure of polymer bonded composites (PBC) are predicted, which further verifies the feasibility and robustness of the developed code in dealing with dynamic impact problems.

Three-Dimensional Numerical Manifold Method for Low-Speed Impact Simulation of PBXs

Three-Dimensional Numerical Manifold Method for Low-Speed Impact Simulation of PBXs

Three-Dimensional Numerical Manifold Method Based on Viscoelastic Constitutive Relation

Abstract In order to accurately and efficiently simulate the dynamic processes of coupled phenomena with viscoelastic, continuous and discontinuous deformations, a three-dimensional (3D) numerical ...

Three-dimensional MLS-based numerical manifold method for static and dynamic analysis

Due to its unique feature for both continuous and discontinuous problems, Numerical Manifold Method (NMM) has made great achievements in many fields in recent years; however, most of them focused on two dimensions. One of the major obstacles for three-dimensional (3D) NMM is the cover generation algorithm, which needs to implement 3D cutting algorithm to generate the physical cover (PC) and manifold elements. In this study, based on the previous 2D Moving Least Squares (MLS) based NMM, a 3D version (denoted as 3D MLS-based NMM) is proposed to bypass the complex preprocessing algorithm. By constructing the mathematical cover (MC) with the influence domains of MLS-nodes, intersection of MC and problem domain is avoided in the generation of the PC, which can significantly simplify the preprocessing. Meanwhile, a regular nodes arrangement can always be employed, which preserves the elegant feature of NMM and also leads to better accuracy. Apart from static problems, free and forced vibration problems, seldom touched by 3D NMM, are also analyzed. Several numerical examples are presented to validate the effectiveness and accuracy of the proposed method. The results show that 3D MLS-based NMM has high accuracy, continuous stress field and excellent convergence rate.

A Modified Symmetric and Antisymmetric Decomposition-Based Three-Dimensional Numerical Manifold Method for Finite Elastic–Plastic Deformations

There are relatively few studies on large rotation or deformation by means of the three-dimensional (3D) numerical manifold method (NMM). A new modified symmetric and antisymmetric decomposition (MSAD) theory is developed and implemented into the 3D NMM, eliminating the false-volume expansion and false-rotation strain/stress problems. The Jaumann rate is used to measure the material rotation, and the geometric stiffness built on the Jaumann rate is deduced. The incremental formulas of the MSAD-based 3D NMM and a practical guide on the implementation of the MSAD theory are given in detail and exemplified. The new theory and formulas can be applied to analyze both large rotation and large deformation problems. Based on the hypoelasto-plasticity theory and the unified strength theory, the unified yield criterion with associated flow rule is implemented into the MSAD-based 3D NMM. Several typical examples are studied, showing the advantage and potential of the new MSAD theory and the MSAD-based 3D NMM.

A high-order three-dimensional numerical manifold method enriched with derivative degrees of freedom

A three-dimensional (3D) high-order numerical manifold method (NMM) is developed based on the partition of unity method (PUM). We enrich the high-order NMM by introducing the derivative degrees of freedom associated with explicit physical significance. The global displacement in the formulation is approximated by a second-order approximation for the local displacement in conjunction with a first-order weight function. This not only helps the high-order NMM effectively avoid the problem of linear dependence that is frequently encountered in the PUM, but also renders the stress or strain at the star points continuous for the high-order NMM without the necessity of further smoothing operation. The effectiveness and robustness of the proposed new high-order NMM are demonstrated by several typical examples. Future potential developments and applications of the method are discussed.

Research on Fault Cutting Algorithm of the Three-Dimensional Numerical Manifold Method

AbstractThe fault cutting algorithm is important when applying the three-dimensional numerical manifold method to engineering simulation. This paper presents a primary approach to the fault cutting algorithm, including data structures, fault cutting procedures, and some basic computing algorithms. First, the data structures of the physical elements and mathematical covers are proposed as single linked lists and linked list arrays, respectively. This reduces the complexity of the algorithm and increases the efficiency when connecting physical elements to covers. Second, a strategy of recording cutting traces between every two faults to ensure that the model agrees with the actual situation was proposed. This strategy also reduces the complexity and improves the efficiency. Third, the mathematical covers and physical elements are cut with all faults independently to process complete cutting instances in a multiblock form and incomplete cutting instances without forming any new irrational block. Finally, fou...

Researches on the Generation of Three-Dimensional Manifold Element under FEM Mesh Cover

Three-dimensional manifold element generation and contact detection algorithm between blocks are the bottleneck for the development of three-dimensional numerical manifold method (NMM). For building mathematics cover, the technology of three-dimensional finite element mesh generation is utilized in the paper. Aiming at the characteristics of complex formation and difficult identification of three-dimensional manifold block, three-dimensional manifold cutting technology is developed. It is important to achieve the coding of mathematical cover (MC) and physical cover (PC) for NMM, which directly determines the correctness of three-dimensional manifold element generation. Based on the character that the coding of three-dimensional manifold is the same as two-dimensional field essentially, coding algorithm of PC system proposed by Dr. Shi is extended to be three-dimensional. A three-dimensional manifold cutting program 3D MC.f90 is developed in this paper, which can generate an arbitrary three-dimensional manifold element under tetrahedral and hexahedral mesh cover. Several examples are made, and results show that three-dimensional manifold block shape and the coding of manifold node and element generated by three-dimensional manifold cutting program all agree well with the definition of three-dimensional manifold element.

Development of contact algorithm for three-dimensional numerical manifold method

SUMMARY This paper customizes a contact detection and enforcing scheme to fit the three-dimensional (3-D) numerical manifold method (NMM). A hierarchical contact system is established for efficient contact detection. The mathematical mesh, a unique component in the NMM, is utilized for global searching of possible contact blocks and elements, followed by the local searching to identify primitive hierarchies. All the potential contact pairs are then transformed into one of the two essential entrance modes: point-to-plane and crossing-lines modes, among which real contact pairs are detected through a unified formula. The penalty method is selected to enforce the contact constraints, and a general contact solution procedure in the 3-D NMM is established. Because of the implicit framework, an open-close iteration is performed within each time step to determine the correct number of contact pairs among multi-bodies and to achieve complete convergence of imposed contact force at corresponding position. The proposed contact algorithm extensively utilizes most of the original components of the NMM, namely, the mathematical mesh/cells and the manifold elements, as well as the external components associated with contacts, such as the contact body, the contact facet and the contact vertex. In particular, the utilization of two mutually approaching mathematical cells is efficient in detecting contacting territory, which makes this method particularly effective for both convex and non-convex bodies. The validity and accuracy of the proposed contact algorithm are verified and demonstrated through three benchmark problems. Copyright © 2013 John Wiley & Sons, Ltd.

Development of three-dimensional numerical manifold method for jointed rock slope stability analysis

This paper presents a three-dimensional numerical manifold method (NMM) for jointed rock slope stability analysis. The main barriers for realistic rock slope stability analysis are discussed, and the unique features of the NMM which make it stand out in slope analysis are emphasized. The framework of the 3-D NMM is established via a regularly-patterned tetrahedral mesh-based mathematical cover system. A contact detection algorithm is then customized to fit the 3-D NMM characteristics. The developed code is first calibrated by two simple cases: inclined plane sliding and tetrahedral wedge sliding, and then applied to a more complex slope scenario. The complete failure process involving large displacement and rotation of multiple interaction blocks is exhibited dynamically. Two typical stabilization/protection techniques are also investigated. The developed 3-D NMM could be potentially used to find the trigger/failure mechanism of jointed rock slopes, so as to optimize the slope stabilization or protection design.

Modeling Unconfined Seepage Flow Using Three-Dimensional Numerical Manifold Method

Three-dimensional numerical manifold method for unconfined seepage analysis is proposed in this article. By constructing hydraulic potential functions of the manifold element, the element conductivity matrix and the global simultaneous equations for unconfined seepage analysis are derived in detail. The algorithm of locating the free surface and the formula for seepage forces are also given. Three-dimensional manifold method employs the tetrahedral mathematical meshes to cover the whole material volume. In the iterative process for locating the free surface, the manifold method can achieve an accurate seepage analysis of the saturated domain below the free surface with mathematical meshes unchanged. Since the shape of manifold elements can be arbitrary, the disadvantage of changing the permeability of transitional elements cut by the free surface in the conventional Finite Element Method (FEM) is removed, and the accuracy of locating the free surface can be ensured. Furthermore, the seepage force acting on the transitional elements can be accurately calculated by the simplex integration. Numerical results for a typical example demonstrate the validity of the proposed method.

A three-dimensional numerical manifold method based on tetrahedral meshes

A three-dimensional NMM based on tetrahedral meshes is developed in this paper. First, the displacement functions of manifold elements are formulated by the partition of unity function. Then, the global equilibrium equations for three-dimensional elasto-statics problem are established by minimizing the total potential energy. The stiffness matrix, loading matrix, displacement resistance matrix are derived for program coding. Thereafter, the computational cost of the global stiffness matrix in the NMM is discussed and compared with that in the classical finite element techniques. Finally, two typical examples are investigated to demonstrate the validity of the proposed method. The results indicate that an enough accuracy of approximation will be obtained with decreasing size of the mathematical mesh. The proposed method can be used as potentially powerful tool for three-dimensional structural analysis.

Three-Dimensional Numerical Manifold Method Based on Hexahedron Element with Full First-Order Cover Function and its Application in Underground Excavation

In this paper, three-dimensional(3D) Numerical Manifold Method (NNM) based on hexahedron element cover with full first-order cover function is proposed and the shape function of C8 isoparametric element in FEM is used as the cover weight function. All sub-matrices in equilibrium equations, including stiffness matrix, initial stress matrix, point force matrix, surface force matrix, body force matrix, inertia force matrix, contact matrix and friction matrix, are derived. Different with 2D contact, the direction of shear stiffness and friction force can not be easily defined in 3D contact. A new iterative method based on vector theory to detect the contact direction is developed. The application of 3D NMM in underground excavation is also presented and show good agreement with real engineering.

Formulation of a Three-dimensional Numerical Manifold Method with Tetrahedron and Hexahedron Elements

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.

Theoretical study of three-dimensional numerical manifold method

The three-dimensional numerical manifold method(NMM) is studied on the basis of two-dimensional numerical manifold method. The three-dimensional cover displacement function is studied. The mechanical analysis and Hammer integral method of three-dimensional numerical manifold method are put forward. The stiffness matrix of three-dimensional manifold element is derived and the dissection rules are given. The theoretical system and the numerical realizing method of three-dimensional numerical manifold method are systematically studied. As an example, the cantilever with load on the end is calculated, and the results show that the precision and efficiency are agreeable.