Meshfree Particles Methods Research Papers (original) (raw)

In the present work we present a meshless natural neighbor Galerkin method for the bending and vibration
analysis of plates and laminates. The method has distinct advantages of geometric flexibility of
meshless method. The compact support and the connectivity between the nodes forming the compact
support are performed dynamically at the run time using the natural neighbor concept. By this method
the nodal connectivity is imposed through nodal sets with reduced size, reducing significantly the computational
effort in construction of the shape functions. Smooth non-polynomial type interpolation functions
are used for the approximation of inplane and out of plane primary variables. The use of nonpolynomial
type interpolants has distinct advantage that the order of interpolation can be easily elevated
through a degree elevation algorithm, thereby making them suitable also for higher order shear deformation
theories. The evaluation of the integrals is made by use of Gaussian quadrature defined on background
integration cells. The plate formulation is based on first order shear deformation plate theory.
The application of natural neighbor Galerkin method formulation has been made for the bending and free
vibration analysis of plates and laminates. Numerical examples are presented to demonstrate the efficacy
of the present numerical method in calculating deflections, stresses and natural frequencies in comparison
to the Finite element method, analytical methods and other meshless methods available in the
literature.

- by Amirtham Rajagopal and +1
- •
- Computational Mechanics, Meshfree Methods, Composite Materials and Structures, Composites

We present a natural element method to treat
higher-order spatial derivatives in the Cahn–Hilliard equation.
The Cahn–Hilliard equation is a fourth-order nonlinear
partial differential equation that allows to model phase separation
in binary mixtures. Standard classical C0-continuous
finite element solutions are not suitable because primal variational
formulations of fourth-order operators are well-defined
and integrable only if the finite element basis functions are
piecewise smooth and globally C1-continuous. To ensure
C1-continuity, we develop a natural-element-based spatial
discretization scheme. The C1-continuous natural element
shape functions are achieved by a transformation of the
classical Farin interpolant, which is basically obtained by
embedding Sibsons natural element coordinates in a
Bernstein–Bézier surface representation of a cubic simplex.
For the temporal discretization, we apply the (second-order
accurate) trapezoidal time integration scheme supplemented
with an adaptively adjustable time step size. Numerical
examples are presented to demonstrate the efficiency of the
computational algorithm in two dimensions. Both periodic
Dirichlet and homogeneous Neumann boundary conditions
are applied. Also constant and degenerate mobilities are considered.We demonstrate that the use of C1-continuous natural
element shape functions enables the computation of topologically
correct solutions on arbitrarily shaped domains

In the present paper the study of the two-dimensional flow field past a circular cylinder for Reynolds number up to 5 · 10 5 is addressed. A Lagrangian particle method approach has been exploited and the simulations have been performed with high spatial resolutions in order to resolve all the main vortical scales. Long simulation time evolutions have been performed in order to get the vortex shedding dynamics as well as the Fourier analysis of the loads. The adopted numerical method allows to discuss both local (boundary layer and near wake dynamics) and global (far wake dynamics) aspects of the problem. The fundamental aspects related to the different identified flow states as well as the drag crisis mechanism are investigated.

A solid-shell MLPG approach for the numerical analysis of plates and shells is presented. A special attention is devoted to the transversal shear locking effect that appears in the structure thin limit. The theoretical origins of shear locking in the purely displacement-based approach are analyzed by means of the consistency paradigm. It is shown that the spurious constraints appear in the constrained strain field, which lead to the appearance of shear locking and sub-optimal convergence rates. The behaviour of the mixed MLPG approach in the thin limit is also considered. It is determined that in the mixed paradigm the Kirchhoff-Love conditions have to be satisfied only at the nodes to avoid the shear locking effects. The validity of the theoretical predictions is supported by the presented numerical examples, where good convergence and accuracy are obtained even if the low-order meshless approximations are used.

A new mixed meshless formulation based on the interpolation of both strains and displacements has been proposed for the analysis of plate deformation responses. Kinematics of a three dimensional solid is adopted and discretization is performed by the nodes located on the upper and lower plate surfaces. The governing equations are derived by employing the local Petrov-Galerkin approach. The approximation of all unknown field variables is carried out by using the same Moving Least Squares functions in the in-plane directions, while linear polynomials are applied in the transversal direction. The shear locking effect is efficiently minimized by interpolating the strain field independently from the displacements. The Poisson's thickness locking phenomenon is eliminated by introducing a new procedure based on the modification of the nodal values for the normal transversal strain component. The numerical efficiency of the derived algorithm is demonstrated by the numerical examples.

Flow behaviour of semi-solid materials is essential to assist the industrial application in Semi-Solid Forging (SSF) technology. From last decade, mesh free methods have grown to simulate high viscous flow pattern with large deformation. In this study, a moving particle explicit method is used to simulate liquid and semi-solid phases of aluminium alloy applied to an impression-die SSF process in a box cavity. Thermal and flow simulation programs based on Lagrangian method are combined considering temperature-viscosity dependency. The morphology of semi-solid material is temperature dependent; it is described by a high viscous model that undergoes plastic deformation. The material flow behaviour in SSF process is investigated for various values of die speed, die temperature, friction and aluminium slurry weight. The deformation characteristics were found in good agreement with the short shot experiments performed. Particularly, the flow pattern corresponding to the die shape and temperature would lead to more accurate prediction of material flow behaviour and required weight to forge the semi-solid material. Further development of the mathematical model and numerical calculation techniques is necessary for flow prediction, die design and investigation of material behaviour when SSF is employed with arbitrary die.

An efficient meshless formulation based on the Local Petrov-Galerkin approach for the analysis of shear deformable thick plates is presented. Using the kinematics of a three-dimensional continuum, the local symmetric weak form of the equilibrium equations over the cylindrical shaped local sub-domain is derived. The linear test function in the plate thickness direction is assumed. Discretization in the in-plane directions is performed by means of the moving least squares approximation. The linear interpolation over the thickness is used for the in-plane displacements, while the hierarchical quadratic interpolation is adopted for the transversal displacement in order to avoid the thickness locking effect. The numerical efficiency of the proposed meshless formulation is illustrated by the numerical examples. keyword: meshless formulation, thick plates, threedimensional solid concept, moving least squares approximation.

This paper numerically studies the interaction of a flowing granular material with an entrainable granular bed, while materials are mixed at the interface of two materials. The rheological behavior of this granular mixture is characterized by a generalized viscoplastic model that includes local volume fraction of materials as well as their physical properties, i.e. size, density, and friction angle. Additionally, the effect of the dynamics of entrained bedtype particles on the rheology of the granular mixture is considered. The governing equations of the flow are discretized using the Incompressible Smoothed Particle Hydrodynamics (SPH) method in which mixing of particles can be conveniently simulated. Two benchmark problems, with and without entrainment, are solved to assess the accuracy of the underlying computational procedure in the absence of mixing. Some other test cases are also solved by including the mixing effect, and the effect of various model parameters is studied. Variations in momentum, maximum velocity, and total kinetic energy of flow with time are reported, and some physical interpretations are presented.

- by Mohammad Nikooei
- •
- Viscoplasticity, Granular Flow, Landslides, Debris Flows

Purpose -The purpose of this paper is to explore the application of the mesh-free local radial basis function collocation method (RBFCM) in solution of coupled heat transfer and fluid-flow problems. Design/methodology/approach -The involved temperature, velocity and pressure fields are represented on overlapping five nodded sub-domains through collocation by using multiquadrics radial basis functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBFs. The energy and momentum equations are solved through explicit time stepping. Findings -The performance of the method is assessed on the classical two dimensional de Vahl Davis steady natural convection benchmark for Rayleigh numbers from 10 3 to 10 8 and Prandtl number 0.71. The results show good agreement with other methods at a given range. Originality/value -The pressure-velocity coupling is calculated iteratively, with pressure correction, predicted from the local mass continuity equation violation. This formulation does not require solution of pressure Poisson or pressure correction Poisson equations and thus much simplifies the previous attempts in the field.

- by Bozidar Sarler
- •
- Engineering, Thermodynamics, Convection, Computational Fluid Dynamics

We present a natural element method to treat higher-order spatial derivatives in the Cahn-Hilliard equation. The Cahn-Hilliard equation is a fourth-order nonlinear partial differential equation that allows to model phase separation in binary mixtures. Standard classical C 0 -continuous finite element solutions are not suitable because primal variational formulations of fourth-order operators are well-defined and integrable only if the finite element basis functions are piecewise smooth and globally C 1 -continuous. To ensure C 1 -continuity, we develop a natural-element-based spatial discretization scheme. The C 1 -continuous natural element shape functions are achieved by a transformation of the classical Farin interpolant, which is basically obtained by embedding Sibsons natural element coordinates in a Bernstein-Bézier surface representation of a cubic simplex. For the temporal discretization, we apply the (second-order accurate) trapezoidal time integration scheme supplemented with an adaptively adjustable time step size. Numerical examples are presented to demonstrate the efficiency of the computational algorithm in two dimensions. Both periodic Dirichlet and homogeneous Neumann boundary conditions are applied. Also constant and degenerate mobilities are con-A. Rajagopal · P. Fischer · P. Steinmann (B) Chair sidered. We demonstrate that the use of C 1 -continuous natural element shape functions enables the computation of topologically correct solutions on arbitrarily shaped domains.

Solid object water entry is a common problem in various natural, industrial and military applications, which involves large deformation of free surfaces and violent fluid-structure interactions. In computational fluid dynamics (CFD), this is a type of problem that tests the robustness and capacity of any CFD numerical algorithm. In this work, the newly-developed updated Lagrangian particle hydrodynamics (ULPH) method, which is a fluid version of peridynamics, is enhanced and applied to simulate solid object water entry problems. ULPH method is Lagrangian meshfree particle method that can ensure the specific free surface conditions automatically satisfied. The density filter and artificial viscosity diffusion are adopted in the ULPH scheme to stabilize and smooth the pressure field. In the process of a rigid body entering water, it may induce negative pressure in some areas of impact region, which can cause spurious tensile instability in some meshfree particle simulations, such as SPH and ULPH. A tensile instability control technique based on the ULPH framework has been developed to overcome the numerical instability. To validate the stability and accuracy of the ULPH approach in simulating water entry problems, several 2D and 3D examples of water entry have been carried out in this work. The necking and cavity pinch-off phenomena are visible in the numerical results. The simulation results of the ULPH method are well compared with experimental data and other numerical solutions. The water crown, cavity shapes and stream pattern formed around the rigid body entering the water can be well captured. The computation results show that the ULPH method has the ability to simulate the complex solid object water entry precess accurately.

- by Jiale Yan and +1
- •
- Smoothed Particle Hydrodynamics, Meshfree Particles Methods

This paper surveys some of the fundamental properties of symplectic integration schemes for classical mechanics and particle methods in particular. The widely used Störmer-Verlet method is discussed in detail and implications of conservation of symplecticity on long term simulations are outlined. The second part of the paper describes the application of a Lagrangian particle method and the Störmer-Verlet time integrator to numerical weather prediction (NWP). A simple vertical slice model and non-hydrostatic flow over orography are discussed in detail.

A numerical model for bottle forming simulation is proposed. It is based upon the Particle Finite Element Method (PFEM) and is developed for the simulation of bottles characterized by rotational symmetry. The PFEM strategy is adapted to suit the problem of interest. Axisym-metric version of the formulation is developed and a modified contact algorithm is applied. This results in a method characterized by excellent computational efficiency and volume conservation characteristics. The model is validated. An example modelling the final blow process is solved. Bottle wall thickness is estimated and the mass conservation of the method is analysed.

- by Pavel Ryzhakov
- •
- Glass Manufacture, Glass Blowing, Meshfree Particles Methods

DualSPHysics is a hardware accelerated Smoothed Particle Hydrodynamics code developed to solve free-surface flow problems. DualSPHysics is an open-source code developed and released under the terms of GNU General Public License (GPLv3). Along with the source code, a complete documentation that makes easy the compilation and execution of the source files is also distributed. The code has been shown to be efficient and reliable. The parallel power computing of Graphics Computing Units (GPUs) is used to accelerate DualSPHysics by up to two orders of magnitude compared to the performance of the serial version.

This paper presents a new concurrent atomistic-continuum method called the atom collocation method (ACM). By adopting the framework of continuum collocation method, ACM aims at overcoming the current difficulties in interfacial mismatch, adaptive analysis, and parallel implementation of existing atomistic-continuum methods. The proposed ACM is truly meshfree and generalizes the full atomistic description, which naturally yields a perfectly compatible atomistic/continuum interface that eliminates any ghost forces. A unique feature of ACM is that the collocation atoms can be turned on or off freely at any time without the need to reconstruct interpolation functions, which greatly enhance the ability to perform adaptive analysis. The proposed ACM is applied to solve problems involving point defect and crack propagation as well as surface, edge, and corner effects and demonstrates excellent accuracy and efficiency compared to molecular statics.

- by Qingcheng Yang
- •
- Materials Science, Multiscale Modelling, Meshfree Particles Methods

This paper presents implementation of higher order PDS (HO-PDS) in FEM framework (HO-PDS-FEM) to solve a boundary value problems involving cracks in linear elastic bodies. Further, an alternative approach based on curl free restriction to extend the current PDS is also presented. This alternative curl-free implementation is scrutinized and compared with a former proposal for HO-PDS whose derivative is not guarantee to satisfy curl free condition. Analysis of traditional plate with a hole problem shows that curl free implementation does not have any specific advantage. Further, techniques for modeling cracks in HO-PDS-FEM are presented. Comparison of two formulations with mode-I crack problem indicates that former proposed HO-PDS-FEM is superior to the proposed curl free formulation, and there is a significant improvement compared to 0 th-order PDS-FEM.

- by Mahendra Kumar Pal and +1
- •
- Finite Element Methods, Continuum Mechanics, Applied Mechanics, Meshfree Particles Methods

Please cite this article in press as: P. Ryzhakov, A modified fractional step method for fluid–structure interaction problems, Rev. int. métodos numér. cálc. diseño ing. 2016. http://dx. a b s t r a c t We propose a Lagrangian fluid formulation particularly suitable for fluid–structure interaction (FSI) simulation involving free-surface flows and lightweight structures. The technique combines the features of fractional step and quasi-incompressible approaches. The fractional momentum equation is modified so as to include an approximation for the current-step pressure using the assumption of quasi-incompressibility. The volumetric term in the tangent matrix is approximated allowing for the element-wise pressure condensation in the prediction step. The modified fractional momentum equation can be readily coupled with a structural code in a partitioned or monolithic fashion. The use of the quasi-incompressible prediction ensures convergent fluid–structure solution even for challenging cases when the densities of the fluid and the structure are similar. Once the prediction was obtained, the pressure Poisson equation and momentum correction equation are solved leading to a truly incompressible solution in the fluid domain except for the boundary where essential pressure boundary condition is prescribed. The paper concludes with two benchmark cases, highlighting the advantages of the method and comparing it with similar approaches proposed formerly.