Search

A particle-plane contact model from the discrete element method has been incorporated into the material point method (MPM) to form an MPs-Mesh scheme for modeling the interactions between soil and boundaries. This scheme enables soil to be simulated with MPM to reflect its large-deformation process and boundaries modeled by a series of triangular elements, i.e., some small triangular planes, to describe complex surfaces flexibly. A more realistic contact detection can be achieved by using the particle-plane contact model between the material points and triangular elements, and both accuracy and efficiency can be improved compared to the classical Bardenhagen's contact algorithm in MPM. The accuracy of the contact model is verified using two simple benchmark examples, i.e., a block sliding on an inclined frictional plane and a sphere sliding on an arc-shaped surface, by comparing the simulation results to analytical solutions. A flume test, i.e., dry granular flow impacting a retaining wall, is simulated for further validation. The Xinmo landslide is also simulated to validate its reliability in engineering-scale soil-boundary interaction problems. The proposed MPs-Mesh scheme allows for complex boundaries to be easily modeled, and interactions between soil and boundaries to be captured and calculated accurately and efficiently, thus solving natural and engineering problems. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract In this paper, we present a novel surface mesh generation approach that splits B-rep geometry models into isotropic triangular meshes based on neural networks and splitting lines. In the first stage, a recursive method is designed to generate plentiful data to train the neural network model offline. In the second stage, the implemented mesh generator, ISpliter, maps each surface patch into the parameter plane, and then the trained neural network model is applied to select the optimal splitting line to divide the patch into subdomains continuously until they are all triangles. In the third stage, ISpliter remaps the 2D mesh back to the physical space and further optimizes it. Several typical cases are evaluated to compare the mesh quality generated by ISpliter and two baselines, Gmsh and NNW-GridStar. The results show that ISpliter can generate isotropic triangular meshes with high average quality, and the generated meshes are comparable to those generated by the other two software under the same configuration.

Two novel plate-bending elements are developed and investigated in this study. Elements with 13 and 15 degree-of-freedoms are named AT13 and AT15, respectively. These triangular elements are formulated in a semi-analytic way. For this aim, the basic elasticity function is employed with unknown parameters. Subsequently, the trial-and-error procedure is used to determine the unidentified constants. Besides, the achieved results are compared with those obtained by displacement-based triangular elements with the same degrees-of-freedom (TUBA13 and TUBA15). In this research, both stress and displacement responses of diverse structures are assessed. After performing extensive numerical studies, the findings clearly demonstrate the superiorities of the proposed elements. [ABSTRACT FROM AUTHOR]

Concrete shells are widespread in civil engineering constructions. Because of the moldability of concrete, special structures such as domes, bridge caissons, buried or raised reservoirs, and arch dams are built with concrete. In this study, we are particularly interested in the variation of the thickness and the resulting strains during a short-term mechanical loading of a concrete ring in its elastic phase. On the one hand, transverse stresses through the thickness are calculated numerically by implementing a particular family of finite elements (four degrees of freedom per summit node) with a two-dimensional shell model, which accounts for thickness variations and transverse distortions. On the other hand, an experimental device was mounted in order to validate numerical predictions.

In this paper, we present a novel surface mesh generation approach that splits B-rep geometry models into isotropic triangular meshes based on neural networks and splitting lines. In the first stage, a recursive method is designed to generate plentiful data to train the neural network model offline. In the second stage, the implemented mesh generator, ISpliter, maps each surface patch into the parameter plane, and then the trained neural network model is applied to select the optimal splitting line to divide the patch into subdomains continuously until they are all triangles. In the third stage, ISpliter remaps the 2D mesh back to the physical space and further optimizes it. Several typical cases are evaluated to compare the mesh quality generated by ISpliter and two baselines, Gmsh and NNW-GridStar. The results show that ISpliter can generate isotropic triangular meshes with high average quality, and the generated meshes are comparable to those generated by the other two software under the same configuration. [ABSTRACT FROM AUTHOR]

This study aims to improve the performance of thermoelastic triangular elements. New triangular elements are proposed with different degrees of freedom. Plane stress models are developed to simulate the complex evolution of structures under external force and thermal conditions. First of all, the structure is analyzed based on the established complementary energy function. In this scheme, the Airy stress function is implemented. The performances of plane stress problems are found by a type of analytical solution. Consequently, the obtained equations are rewritten in terms of the nodal values. After suggesting new elements, extensive analyses for the plane stress problems were performed, and the numerical studies validated the proper behavior of the novel elements. The obtained results clearly showed that the new procedure led to precisions of structural deformation and stresses. In this investigation, different benchmarks, such as small patches, cantilever beams, thick curved beams, non-prismatic cantilever beams, and thin plates, were evaluated. Problems are solved under different loading conditions, including mechanical load, thermal load, and a combination of mechanical–thermal loads. The analytical trial function approach for the construction of an eight-node plane element is used because the formulations are identical. This study helps to find the near-exact values of different responses under the influence of thermal load in addition to external loading, including both displacement and stress outcomes. [ABSTRACT FROM AUTHOR]

The thin-film antenna is in a state of high-speed rotation in space, and studying the influence of its structure size on its vibration characteristics can avoid the occurrence of resonance. The rotational vibration characteristics of thin film antenna are studied by using the Absolute Nodal Coordinate Formulation (ANCF) with improved computational efficiency. The triangular element is used to mesh the thin film antenna, the kinetic energy, strain energy and external force potential energy of the element are calculated. The mass matrix and stiffness matrix of the element are transformed into the overall mass matrix and stiffness matrix through Boolean matrix. According to the rotation equivalent model, the centrifugal force potential energy generated by the high-speed rotation of the thin film antenna is transformed into the centrifugal force stiffness matrix. The relationship between rotational speed and natural frequency of thin film antenna under different structural sizes is analyzed. By analyzing the critical speed generated by the front traveling wave and the back traveling wave, the theoretical basis for the structural design of thin film antenna is improved.

This paper proposes a method for creating finite elements with simultaneous approximation of functions corresponding to displacements and rotations. New triangular and quadrangular finite elements have been created, which can have additional nodes on the sides. No locking effect is observed for all the created elements. All created elements retain the existing symmetry of the design models. The results of numerical experiments are presented.

A second-order control volume finite element method combined with the multiscale flux approximation (CVFEM-MS) based on triangular elements is proposed to numerically investigate the self-heating effects of semiconductor devices. The multiscale fluxes are combined with a selected set of second-order vector basis functions to stabilize the discretization of carrier continuity equations with respect to triangular elements. Numerical results reveal that the proposed method is robust and accurate, even on the mesh of low-quality, where the detrimental impacts caused by the severe self-heating on the terminal currents can be obviously observed for a bipolar transistor model. [ABSTRACT FROM AUTHOR]

To obtain proper stresses , three new triangular elements are formulated in this study. First, a complementary energy functional is used within an element for the analysis of plane problems. In this energy manifestation, the Airy stress function will be applied as a functional variable. Then, some basic analytical solutions are assigned for the stress functions. These trial functions are matched with each element number of degrees of freedom. The result is a number of equations with anonymous constants. Subsequently, according to the principle of minimum complementary energy, the unknown constants can be expressed in terms of displacements. Finally, this system can be rewritten in terms of the nodal displacement. In this way, three new triangular elements are formulated. To validate the results, extensive numerical studies are performed. The findings clearly demonstrate accuracies of structural displacements as well as stresses. [ABSTRACT FROM AUTHOR]

Twelve new finite elements with drilling degrees of freedom have been developed: triangular and quadrangular elements based on a modified hypothesis about the value of approximating functions on the sides of the element, which made it possible to avoid dimensional instability when all rotation angles are zero; incompatible and compatible triangular and quadrangular elements which can have additional nodes on the sides. Approximating functions satisfy the following condition: the value of the rotational degree of freedom of a node is nonzero and equal to one only for one of them. Numerical examples illustrate estimated minimum orders of convergence for displacements and stresses. All created elements retain the existing symmetry of the design models.

Recently, many literature studies have focused on the development on new elements in finite elements. This paper aims to develop a new quadrature for the 3-node triangular element for the purpose of evaluation of element stiffness matrix. The analysis of triangular element is usually done in a quadrilateral element by dividing the quadrilateral element into two. The edge sampling point quadrature is a mimics of Gauss numerical integration scheme. This sampling integration scheme consists of five sampling points and weights where four sampling points are at the edge and one at the center of the element. Accuracy of results, convergence of the results and stability of values have been tested using the standard benchmarked problems defined by various research studies. [ABSTRACT FROM AUTHOR]

In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathematical formulation. Additionally, the Jacobian matrix for the second order derivatives was simplified and used to derive each element’s strain-displacement matrix in bending. The elements were compared using carefully selected elastic and aero-elastic bench mark problems, regarding the number of elements needed to reach convergence, the resulting accuracy, and the needed computation time. The best suitable element for elastic free vibration analysis was found to be the Linear Quadrilateral Element with deformation-based shape functions, whereas the most suitable element for stress analysis was the 8-Node Quadrilateral Element, and the most suitable element for aero-elastic analysis was the 9-Node Quadrilateral Element. Although the linear triangular element was the last choice for modal and stress analyses, it establishes more accurate results in aero-elastic analyses, however, with much longer computation time. Additionally, the nine-node quadrilateral element was found to be the best choice for laminated composite plates analysis.

In this paper, three new triangular fully parameterized thick plate/shell elements are proposed based on the absolute nodal coordinate formulation. The volume parameters and corresponding independent volume gradient vectors are used to simplify the element construction. The node-wise structural parameter is adopted to circumvent the slope discontinuity issue associated with the volume gradient vectors. Two three-node elements inherit the interpolation strategy in the membrane direction of a well verified thin plate element. For the thickness direction, linear and quadratic interpolation are used in the three-node elements. Inspired by the quadrilateral plate elements with gradient vectors only along thickness direction, a six-node triangular element is presented with quadratic interpolation in both membrane and thickness direction. Three static analyses with large deformation and one dynamic analysis are conducted to evaluate the performance of the new elements. It concludes that the three-node element with linear interpolation in the thickness direction performs not well due to the incompatible/low interpolation in the thickness direction. The other two elements show good accuracy in all the numerical tests. Though the six-node element exhibits slightly higher accuracy than the quadratic three-node element, its DOFs are much more than the quadratic three-node element, which makes it less attractive. • ANCF thick triangular elements with ability to model initially curved shell structure. • Straightforward transformation between the element and the Bézier triangular patch. • A 6-node higher order element without the volume gradient slope discontinuity issue is constructed. • New elements exhibit higher accuracy compared with the existing ANCF thick triangular elements. [ABSTRACT FROM AUTHOR]

A Simple three-node Discrete Kirchhoff Triangular (SDKT) plate bending element is proposed in this study to overcome some inherent difficulties and provide efficient and dependable solutions in engineering practice for thin plate structure analyses. Different from the popular DKT (Discrete Kirchhoff Theory) triangular element, using the compatible trial function for the transverse displacement along the element sides, the construction of the present SDKT element is based on a specially designed trial function for the transverse displacement over the element, which satisfies interpolation conditions for the transverse displacements and the rotations at the three corner nodes. Numerical investigations of thin plate structures were conducted, using the proposed SDKT element. The results were compared with those by other prevalent plate elements, including the analytical solutions. It was shown that the present element has the simplest explicit expression of the nine-DOF (Degree of Freedom) triangular plate bending elements currently available that can pass the patch test. The numerical examples indicate that the present element has a good convergence rate and possesses high precision.

Abstract A differential quadrature hierarchical finite element method (DQHFEM) using Fekete points was formulated for triangles and tetrahedrons and applied to structural vibration analyses. First, orthogonal polynomials on triangles and tetrahedrons that can be used as bases of the hierarchical finite element method (HFEM) were derived and simple formulas of transforming one dimensional non-uniform nodes to simplexes were presented. Then the non-uniform nodes were used as initial guesses to solve the Fekete points on simplexes through Newton–Raphson's method together with the orthogonal polynomials. New differential quadrature (DQ) rules on simplexes were formulated using the HFEM bases and the Fekete points. The numbers of nodes or bases on different edges and faces and inside the body of the new DQ elements do not relate with each other like the HFEM that can freely assign different numbers of bases on different edges and faces and inside the body. So the new DQ method was named as a differential quadrature hierarchical (DQH) method that uses either interpolation functions or orthogonal polynomials as bases inside the element. Its weak form was named as the DQHFEM. Besides the DQH method and its weak form, a simple method of generating high quality linear and high order triangular and tetrahedral meshes from a single NURBS patch was presented. Numerical tests of the DQHFEM through structural vibration analyses showed that high accuracy results can be obtained using only a few nodes even on curvilinear domains using the DQH bases on both physical and geometric fields. It was concluded that wide applications of the DQH method and the DQHFEM to science and engineering are possible and commercial codes based on them are deserved to be developed. [ABSTRACT FROM AUTHOR]

Abstract This paper reports a constructal investigation of heat transfer in a nonuniform heat generating triangular area, and numerically studies the entropy generation performance over the area inserted with constant and discrete variable cross-sectional high conductive channels (HCCs), respectively. The effects of the nonuniform heat generating (NUHG) coefficient and width coefficient on the overall thermal performance are also analyzed with several conditions of heat distributions. This model has two constraints: the area ratio of HCCs to the whole heat generating area and the global heat generation (the heat is nonuniformly distributed over the area). The structure of the HCCs is free to morph in order to present a better thermal performance. The numerical results show that for an elemental triangle, the optimal structure tends to elongate as the NUHG coefficient increases. It is also indicated that the dimensionless entropy generation rate for the first-order construct constituting of six elements is decreased by 20.0% in comparison with the counterpart constituting of four elements, which means that increasing the number of incorporated elements makes it favorable to improve the overall thermal performance. Additionally, the quartic minimized dimensionless entropy generation rate of the first-order construct with discrete cross-sectional HCCs performs 14.2% better than the counterpart with constant highly conductive routes. In this context, the thermal performance can be improved reasonably by intruding the variable cross-sectional architecture into the heat generating area. In general, the effects of the nonuniform heat generating coefficient p , width coefficient m and the number of triangular elements n on the overall thermal performance are studied. The pivotal innovation of this paper is introducing entropy generation minimization theory into the constructal design of triangular assemblies with both nonuniform heat generation and discrete variable cross-sectional HCCs, which can contribute to the design of practical electronic devices to a promising heat transfer performance. Highlights • A constructal design of in nonuniform heat generating triangular area is performed. • With constant and discrete variable cross-sectional high conductivity channels. • Entropy generation rate is minimized. • Analytical method and finite element method are compared. [ABSTRACT FROM AUTHOR]

Highlights • The thermo-elastic nonlinear analysis of various Functionally Graded shell is studied. • The Voigt's model is adopted to define the Functionally Graded material properties. • A six-noded isoparanetric triangular shell element is presented. • The Euler-Rodrigues formulations and the first-order shear deformation theory are employed. • Thermo-mechanical buckling of FG shell is predicted. • Both the pre-buckling and post-buckling equilibrium paths are traced. Abstract In this paper, the thermo-elastic nonlinear analysis of various Functionally Graded (FG) shells under different loading conditions is studied. A second-order isoparametric triangular shell element is presented for this purpose. The element is six-noded, and each node has all six independent degrees of freedom in space. It should be added, the first-order shear deformation theory is induced. Furthermore, Voigt's model is adopted to define the FG material properties, which are considered to change gradually from one surface to another. The critical temperature is predicted. Both the pre-buckling and post-buckling equilibrium paths are traced. Since the linear eigenvalue analysis leads to wrong responses in the problems with strong nonlinearity, the suggested procedure is performed based on the FEM and more exact estimations are achieved using equilibrium path. [ABSTRACT FROM AUTHOR]

Abstract Super-quadric elements based on continuous function representation can be used to construct the geometric shape of irregular particles accurately. Although the contact detection of these elements has been well established, in real industrial applications, the geometric boundaries are complex and cannot be described by a specific function. A common and popular approach is to use a standard triangular finite-element surface mesh. In this work, the interaction between super-quadric particles and triangular elements is discussed in detail. Because the shapes and surface curvatures differ under the various contact patterns between super-quadricparticles, the linear contact force model cannot be used to calculate the contact force accurately; therefore, a corresponding non-linear force model is extended to super-quadric particles. In this model, the equivalent radius of curvature at a local contact point is introduced to calculate the normal contact force, and the tangential contact force is simplified based on the contact model of the spherical elements. To examine the validity of the algorithms and this model, three tests are performed. The first consists of a comparison against theoretical results for a flat wall impacted by a single cylinder-like particle with different blockiness parameters. In the second, the continuity of the contact force when a particle slides from one triangular element through the shared edge or the shared vertex to the neighboring element is tested. In addition, the three contact modes are counted in a boundary model represented by several triangular elements, and compared with the previous numerical experiments. The last tests consist of comparisons against experimental results of the arch structure of cube-like particles and the dynamic hopper discharge of ellipsoids. These studies demonstrate that the proposed method and force model are reliable and applicable for the dynamic hopper discharge of non-spherical particles. Furthermore, the effects of particle shapes, base angles, and friction coefficients on the discharge rate are discussed. The results show that the discharge rate always decreases with decreasing base angle or increasing blockiness, particle friction, or aspect ratio (from 0.5 to 1.5). Moreover, the influences of the base angle, the friction coefficient, and the blockiness on the flow rate are the primary factors, whereas the aspect ratio has a secondary effect on the flow rate. Finally, the packing fraction and the probability density functions of the normal contact force at the initial moment are analyzed to demonstrate the effect of blockiness on the macroscopic discharge rate. Graphical abstract Unlabelled Image Highlights • The contact detection between super-quadric particles and triangular elements is described. • The non-linear force model considering the equivalent radius of curvature is applied for super-quadric particles. • The contact algorithm and force model are applicable for the dynamic hopper discharge of non-spherical particles. • Ellipsoids, cylinders, and cubes with different aspect ratios and blockiness are modeled. • The effects of particle shapes, base angles, and friction coefficients on the flow rate are discussed. [ABSTRACT FROM AUTHOR]

In this paper, a simple locking-free triangular plate element, referred to here as the Mindlin triangular plate element with full integration (MTPF), is presented for the analysis of cracked thick-thin plates. The element employs a new specially designed incompatible meshless approximation, independent of the nodes and triangle shape, in order to define displacements for the purpose of avoiding the use of reduced/selected integration to make the MTPF locking-free and valid for the thin plate. The current MTPF is also extended for the analysis of cracked thick-thin plates, and the virtual crack closure technique is applied in order to compute the crack tip stress intensity factors of the cracked thick-thin plates, where the formula derivation and numerical implementation are very simple and convenient for the present MTPF. Several representative numerical examples demonstrate that the MTPF is a robust and high-performance element for cracked thick-thin plates. [ABSTRACT FROM AUTHOR]

A nonuniform heat generating model in a triangular area is built in this paper. Constructal optimizations of the models with constant and discrete variable cross-sectional high conductivity channels (HCCs) are performed by choosing minimum maximum temperature difference (MTD) as optimization objective. Optimal constructs of the triangular element and triangular first order assembly (TFOA) are obtained, respectively. The results indicate that for the TFOA with constant cross-sectional HCCs, the minimum MTD is reduced by increasing the nonuniform heat generating (NUHG) coefficient p , namely the heat conduction performance (HCP) is better when more heat generation is generated near the heat sink. The HCP of TFOA is also improved by increasing its complexity of internal structure. Furthermore, the minimum MTD of TFOA with discrete variable cross-sectional HCCs is reduced by 12.57% than that with constant cross-section. Therefore, the HCP of TFOA can be further improved by adopting discrete variable cross-sectional structures for the HCCs. The optimization results obtained from numerical calculations can provide some theoretical guidelines for the optimal heat dissipation designs of electronic devices. [ABSTRACT FROM AUTHOR]