Smoothed Point Interpolation Method Research Articles

An SPIM-FEM adapting coupling approach for the analysis of quasi-brittle media

This paper presents an adaptive coupling approach between meshless Smoothed Point Interpolation Methods (SPIMs) and the Finite Element Method (FEM) for the physically nonlinear analysis of quasi-brittle media. The nonlinear behaviour is represented by scalar damage and smeared-crack models. In the proposed adaptive coupling approach, the domain is initially discretised with a relatively coarse FEM mesh. During the solution process, FEM patches are replaced by meshless discretisations according to certain selection criteria. Refinement is also considered.

Numerical study of interactions between Bingham fluids and flexible structures using the immersed boundary-lattice Boltzmann method

This paper studies the interactions between Bingham fluids and flexible structures under an immersed boundary lattice-Boltzmann framework. The objective of this paper is to understand the rheology effects of Bingham fluids on the structure responses and the flow characteristics within Bingham fluids–structure interactions. To this end, a numerical algorithm that integrates the lattice Boltzmann method and the smoothed point interpolation method is proposed. Alongside this, a hybrid multiple relaxation time scheme in the framework of the immersed boundary-lattice Boltzmann method is used to improve the numerical accuracy and stability. Then, the numerical algorithm is applied to three typical fluid–structure interactions cases in both Newtonian and Bingham fluids regarding an elastic beam, a self-induced elastic beam attached to a circular cylinder and a self-propelled fishlike body. Numerical results highlight that the yield stress of Bingham fluids influences predominantly on the structure responses, such as the solid deformation, the oscillation amplitude, the oscillation period, and the swimming velocity. In addition, the yielded/unyielded zones' evolution process of the Bingham fluids–structure interaction is also identified in this paper.

A Smoothed Point Interpolation Method for the Timoshenko Beam

This paper aims to extend the meshless smoothed point interpolation methods (SPIMs) to the analysis of the Timoshenko beam problem. These methods are based on the concepts of smoothing domains and weakened-weak (W2) form; their use is made possible by the extension of the weakened-weak form that they are based on to the case of the Timoshenko beam. The provided numerical simulations emphasize that, by changing the number of nodes used to build the shape functions at each interest point, it is possible to obtain a lower-bound or an upper-bound approximation to the analytical solution of the beam problem. This property is further exploited with the concept of [Formula: see text]PIM shape function that, blending together the different bounds to the analytical solution, allows to improve the convergence. The proposed formulation is naturally locking-free, i.e., no additional treatment is necessary to avoid the spurious stiffer behavior that commonly occurs in FEM simulations of shear-deformable beams.

An h-adaptive edge-based smoothed point interpolation method for elasto-plastic analysis of saturated porous media

This study presents the first application of the edge-based smoothed point interpolation method (ESPIM) for adaptive analysis of coupled elasto-plastic problems in saturated porous media. The original ESPIM is enhanced with an adaptive strategy involving an automated h-refinement scheme, a simple, yet effective, recovery-based error indicator, and an efficient data transfer scheme to analyse coupled elasto-plastic problems in geomechanics. The governing equations are presented and discretised in space and time to yield the fully coupled system of equations. The solution strategy is then discussed in terms of handling the material non-linearity, and accommodating the proposed adaptivity procedure in the numerical algorithm. Four numerical examples comprising two different bearing capacity problems, a two-dimensional consolidation problem, and a slope stability analysis are thoroughly investigated. Different adaptive analyses with a range of adaptivity control parameters are investigated in each example and the performances of different techniques are compared in terms of accuracy and the time of the analysis. The results show the ability of the proposed adaptive analyses in yielding accurate and efficient results. Conclusions are drawn in terms of the most efficient numerical set-up to solve non-linear problems in porous media using the proposed numerical scheme.

Designing an efficient smoothed point interpolation method for modeling slope deformation

PurposeIn this paper, the smoothed point interpolation method (SPIM) is used to model the slope deformation. However, the computational efficiency of SPIM is not satisfying when modeling the large-scale nonlinear deformation problems of geological bodies.Design/methodology/approachIn this paper, the SPIM is used to model the slope deformation. However, the computational efficiency of SPIM is not satisfying when modeling the large-scale nonlinear deformation problems of geological bodies.FindingsA simple slope model with different mesh sizes is used to verify the performance of the efficient face-based SPIM. The first accelerating strategy greatly enhances the computational efficiency of solving the large-scale slope deformation. The second accelerating strategy effectively improves the convergence of nonlinear behavior that occurred in the slope deformation.Originality/valueThe designed efficient face-based SPIM can enhance the computational efficiency when analyzing large-scale nonlinear slope deformation problems, which can help to predict and prevent potential geological hazards.

An explicit velocity correction-based immersed boundary-hybrid lattice Boltzmann flux solver for fluid-structure interaction with large solid deformation

In this work, an explicit velocity correction-based Immersed Boundary-Hybrid Lattice Boltzmann Flux Solver (IB-HLBFS) is developed for Fluid-Structure Interaction (FSI) problems with large solid deformation in two-dimensional. The fluid domain is solved by the Lattice Boltzmann Flux Solver (LBFS) while the solid domain is solved by the Smoothed Point Interpolation Method (S-PIM). For coupling the two methods, the Explicit Velocity Correction (EVC) is developed and applied to both the fluid and the solid by implementing the Immersed Boundary Method (IBM). The fluid domain in IB-HLBFS can be discretized with non-uniform mesh so that the efficiency is improved meanwhile the accuracy is ensured compared with the original Lattice Boltzmann Method (LBM). Moreover, the explicit velocity correction simplifies the matrix inversion in the Implicit Velocity Correction (IVC) hence the efficiency is further improved. To show the advantages and the reliability of the present IB-HLBFS, the numerical simulations of flow past the elastic beam, flow past a circular cylinder with a flexible beam behind, and swimming of a self-propelled fishlike body are given to show the application of IB-HLBFS in FSI with complex fluid dynamics and large solid deformation. The results indicate that the present method is advantageous in terms of efficiency and accuracy, and has a wide prospect in engineering applications as well.

Phase-field modelling of brittle fracture with Smoothed Radial Point Interpolation Methods

The phase-field modelling of brittle fracture is an efficient tool for the modelling of complex cracks, since it is capable to predict crack initiation and branching, as well as the merging of cracks. While there are a number of papers in the literature devoted to the application of different meshfree methods to the phase-field modelling of fracture, this paper is, to the authors knowledge, the first application of the methods of the Smoothed Point Interpolation Methods (SPIM) family. The smoothing operation, that is used to approximate the displacements gradient in standard SPIM strategies, is here extended to the additional variable of a phase-field model. A number of numerical simulations, performed considering different kind of smoothing domains and support nodes selection strategies, illustrates the characteristics of the proposed approach.

An Automatic Adaptive Edge-based Smoothed Point Interpolation Method for Coupled Flow-Deformation Analysis of Saturated Porous Media

An adaptive analysis based on an advanced computational method, referred to as edge-based smoothed point interpolation method (ESPIM), is proposed for numerical analysis of coupled problems in geomechanics. For the adaptive procedure, a simple error indicator derived based on the maximum difference of the strain energy among the three nodes of each background cell is adopted along with a simple automatic h-type local refinement strategy and automatic mesh generator based on the Delaunay triangulation. Novel activation and termination criteria are proposed for initiating and ending adaptivity analysis in each time step. The performance of the proposed adaptive procedure is investigated through three numerical examples. The results show that with the proposed adaptivity procedure, the adaptive ESPIMs have better computational efficiency compared to non-adaptive methods or the general uniform mesh refinement strategy. In particular, it is shown that the proposed termination criteria for the refinement steps ensures that the adaptivity procedure stops when the computational cost of the refinement overweights the resulting gain in the solution accuracy (determined by the user), hence unnecessary refinement steps are avoided in the analysis to yield optimal computational efficiency.

A three-dimensional hybrid immersed smoothed point interpolation method for fluid-structure interactions

A three-dimensional hybrid immersed smoothed point interpolation method (3D HIS-PIM) has been developed to handle fluid-structure interactions (FSI) with simple geometries. Incompressible viscous fluid is solved by semi-implicit characteristic-based split method with standard Galerkin discretization, smoothed point interpolation method is employed to solve the motion and deformation of nonlinear solids based on gradient smoothing technique, and the virtual fluid is introduced into the entire solid domain to calculate the FSI force. The proposed method can avoid the fluid mesh adjustments, and allows the use of four-node tetrahedral elements for both fluid and solid domains to simplify the pre-processing for mesh generations. The FSI force condition is imposed with a hybrid force, which uses a form of body force for pressure term and boundary force for shear force. The boundary force accords with the physical law and the body force can ensure the numerical stability. The proposed method works well for FSI problems with moving or largely deformable solids, and can achieve more accurate results using a hybrid force than the fully body force in the original method. A large range of mesh size ratios between fluid and solid meshes is allowed due to the treatment of FSI boundary conditions.

A Lagrangian Point Approximation-Based Immersed Boundary–Lattice Boltzmann Method for FSI Problems Involving Deformable Body

The proposed immersed boundary-lattice Boltzmann method (IB-LBM) with smoothed point interpolation method (S-PIM) has been verified to be an effective tool for simulating complex fluid–structure interaction (FSI) problems in previous works. LBM is employed as fluid solver with a simple solution process, S-PIM is used for largely deformable solids on the basis of gradient smoothing technique, and their combinations for FSI problems are achieved under the framework of immersed boundary method (IBM). IBM allows the coupling method to use a fixed fluid Euler mesh to avoid frequent mesh updates due to the movement or deformation of solids, whereas the introduction of fictitious fluid causes the internal mass effect and yields numerical errors. An extended Lagrangian point approximation approach has been proposed and introduced in IB-LBM with S-PIM to tackle this issue, and numerical experiments for FSI problems associated with rigid movement and large deformation of solids are investigated. It is verified that the accuracy and convergency properties of the present method are significantly improved compared with the original one in which the mass effect was not considered.

A ghost-node immersed smoothed point interpolation method (ghost-node-ISPIM) for fluid-structure interaction problems

Immersed smoothed point interpolation method (IS-PIM) was successfully proposed for solving fluid-structure interaction (FSI) problems with large solid deformations. However, the defects of IS-PIM include inaccurate solid boundary, spurious pressure oscillation and the “fresh node” phenomenon, which will cause different degrees of numerical errors. In order to solve these problems, the ghost-node immersed smoothed point interpolation method (Ghost-node-ISPIM) has been presented in this paper. In this method, the ghost-node technique is firstly proposed and achieved based on unstructured triangular elements, combined with mass source/sink algorithm and the sharp-interface method to fix the inherent defects existed in original IS-PIM. The effectiveness and superiority of the Ghost-node-ISPIM are demonstrated by a series of typical FSI numerical examples.

Particle node-based smoothed point interpolation method with stress regularisation for large deformation problems in geomechanics

In this study, a new numerical scheme is developed for modelling large deformation problems in geomechanics. The approach is based on employing the node based smoothed point interpolation methods (NSPIMs) in the framework of the particle finite element method (PFEM). The proposed technique is particle based in the sense that all variables are computed and stored at the nodes, hence constant transformation of the information between Gauss points and nodes, which is required in the particle finite element method (PFEM), is avoided. The accuracy of the proposed technique and its possible numerical instabilities, inherited through the use of NSPIMs in the method, are investigated in details. Accordingly, two remedial techniques, one based on stress regularisation by moving least square (MLS) and the other based on an improved formulation of NSPIMs, are presented to alleviate the instability problem and improve the accuracy of the numerical solutions. The proposed techniques and measures are thoroughly examined through three numerical examples, and conclusions are drawn.

An improved node-based smoothed point interpolation method for coupled hydro-mechanical problems in geomechanics

An improved version of the node-based smoothed point interpolation methods (NSPIMs) is proposed for coupled hydro-mechanical problems of geotechnical engineering. In the improved NSPIMs (I-NSPIMs), the polygonal nodal smoothing domains are estimated with area-equivalent circular domains. The smoothed strains over the circular nodal smoothing domains are then assumed to be linear, in contrast to the constant smoothed strain adopted in the original NSPIMs. The efficiency of the proposed method is investigated through five practical examples, all showing clear superiority of I-NSPIMs over the original formulation of NSPIMs in small deformation problems of geomechanics.

Comparisons of two representative methods classified as immersed boundary and domain methods

Immersed methods have proven to be powerful numerical measures to simulate intricate fluid-structure interactions using non-conforming meshes. And they can be classified into immersed boundary methods and immersed domain methods based on the utilization of fictitious fluid around the interface or over the entire solid domain. Their performances are compared in light of several common problems for immersed methods, and two representative methods are employed by immersed boundary-lattice Boltzmann method with smoothed point interpolation method (IBLBM-SPIM) and immersed smoothed point interpolation method (IS-PIM). Numerical tests show that IS-PIM allows a fairly independent mesh size for each domain of fluid and solid, and achieves a smooth solid response; IBLBM-SPIM can ensure numerical stability in a large range of density ratio between solid and fluid by setting a proper time step to alleviate the added mass effect, and has a direct influence on the deformation and motion of solids. The present study also gives some enlightening thoughts on developing novel methods to deal with different FSI problems.

Simulating fluid-structure interactions with a hybrid immersed smoothed point interpolation method

In this paper, a hybrid immersed smoothed point interpolation method (hybrid IS-PIM) is proposed, which employs a hybrid force approach to impose fluid-structure interaction (FSI) force condition. Compared with the original IS-PIM using a complete body force, the hybrid IS-PIM still utilizes the form of body force for pressure term to enhance the stability of numerical algorithm, and the shear force is applied to the boundary to accord with the physical law and the practical situation. Numerical examples have shown that the body force term enables the proposed method to overcome the constraint of mesh size ratio, and the boundary force term has a direct effect on the motion and deformation of solids, which yields more accurate results in comparison with the complete body force applied in the original IS-PIM. Moreover, the equivalence of FSI force in forms of body force and boundary force are also verified straightforwardly using a series of mesh combinations.

The hygro-thermo-electro-mechanical coupling edge-based smoothed point interpolation method for the response of functionally graded piezoelectric structure under hygrothermal environment

In this paper, we analyze the hygro-thermo-electro-mechanical (HTEM) coupling problem of functionally graded piezoelectric (FGPE) structure based on edge-based smoothed point interpolation method (ES-PIM). The basic equations for FGPE structure are derived in the multi-physical field. Triangular elements adopted in ES-PIM can be generated automatically and suitable for complicated structures. The responses for the HTEM coupling problem are calculated by ES-PIM and finite element method (FEM) under different hygrothermal conditions. Through the numerical examples, the factors related to the temperature and moisture fields are explored. The exponential factor and the hygrothermal effect on the responses of the FGPE structure are also studied. Besides, the advantages of proposed method for HTEM coupling problems are also validated by several numerical examples. These solutions also indicate that the increase of temperature and moisture concentration decreases the structural stiffness when empirical constants are set to negative numbers, leading to the decrease of frequency and variation of displacement. This article proposes an excellent numerical method and provides a reference for the design and application of piezoelectric structures.

A coupled finite element-meshfree smoothed point interpolation method for nonlinear analysis

In this paper, coupling between the finite element method (FEM) and the smoothed point interpolation methods (SPIM) is employed in the study of inelastic problems where the meshfree methods presents attractive characteristics. These studies are based on a strategy whose inelastic region is previously discretised by a SPIM method, while the rest of domain is represented by FEM. Linear and nonlinear numerical simulations are presented, and the results of simulations are compared, when possible, to analytical solutions and experimental results in order to demonstrate the main features of the proposed coupling.

Thermal Elastic–Plastic Analysis of Three-Dimensional Structures Using Face-Based Smoothed Point Interpolation Method

In this work, a face-based smoothed point interpolation method (FS-PIM) is formulated for three-dimensional (3D) thermal elastic-plastic analysis of structures. For this method, field functions are approximated using second order PIM shape functions and the face-based smoothing domains are used to perform the numerical integration. The material properties are considered to be temperature-dependent and the plastic behavior is studied through the Von Mises yield function. Numerical examples with different kinds of boundary conditions are investigated to verify the validity of the present method. The obtained results indicate that FS-PIM is an effective technique for the thermal elastic-plastic analysis of structures.

Does the upper bound solution property of the Node-based Smoothed Point Interpolation Methods (NSPIMs) hold true in coupled flow-deformation problems of porous media?

It has been shown that a recently developed class of numerical solutions referred to as node-based smoothed point interpolation methods (NSPIMs) can provide an upper bound solution in energy norm for force-driven elasticity problems. In this study, bound solution property of the NSPIMs is examined in plane-strain coupled problems of porous media, to explore how the presence of pore water pressure affects this feature of the NSPIMs. Brief descriptions of the governing differential equations and the formulation of the NSPIMs are first presented, followed by the discretised form of the governing equations. The bound solution properties of three popular NSPIMs in poro-elasticity problems are then thoroughly investigated, both theoretically and numerically, and compared to those of the linear FEM. The results show that the upper bound solution property of the NSPIMs is lost in coupled problems of poro-elasticity due to the coupling effects of the fluid phase.

A [formula omitted]SPH–SPIM coupled method for fluid–structure interaction problems

In this work, the fluid–structure interaction (FSI) problems have been studied by coupling the δ Smoothed Particle Hydrodynamics (δSPH) with the Smoothed Point Interpolation Method (SPIM), which is abbreviated as δSPH–SPIM coupled method. SPIM is used for structure dynamics owing to its good performance for large deformation analysis of solids. For the fluid solver, in order to further reduce the unphysical noise in pressure field, the δSPH (where the density diffusion term is added into the continuity equation) is adopted. Inspired by the particle-element method, a new interpolation scheme is proposed for the coupling force calculation and transfer, which does not require the fluid and solid spacing to be the same. The coupled method has been verified by hydrostatic water column on an elastic plate, and has been applied to solve the problems of high speed water entry of an elastic wedge as well as dam-break flow.