A three-dimensional hybrid smoothed finite element method (H-SFEM) for nonlinear solid mechanics problems

This paper presents a novel three-dimensional hybrid smoothed finite element method (H-SFEM) for solid mechanics problems. In 3D H-SFEM, the strain field is assumed to be the weighted average between compatible strains from the finite element method (FEM) and smoothed strains from the node-based smoothed FEM with a parameter α equipped into H-SFEM. By adjusting α, the upper and lower bound solutions in the strain energy norm and eigenfrequencies can always be obtained. The optimized α value in 3D H-SFEM using a tetrahedron mesh possesses a close-to-exact stiffness of the continuous system, and produces ultra-accurate solutions in terms of displacement, strain energy and eigenfrequencies in the linear and nonlinear problems. The novel domain-based selective scheme is proposed leading to a combined selective H-SFEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed 3D H-SFEM is an innovative and unique numerical method with its distinct features, which has great potential in the successful application for solid mechanics problems.

A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

A node-based smoothed conforming point interpolation method (NS-CPIM) for elasticity problems

This paper formulates a node-based smoothed conforming point interpolation method (NS-CPIM) for solid mechanics. In the proposed NS-CPIM, the higher order conforming PIM shape functions (CPIM) have been constructed to produce a continuous and piecewise quadratic displacement field over the whole problem domain, whereby the smoothed strain field was obtained through smoothing operation over each smoothing domain associated with domain nodes. The smoothed Galerkin weak form was then developed to create the discretized system equations. Numerical studies have demonstrated the following good properties: NS-CPIM (1) can pass both standard and quadratic patch test; (2) provides an upper bound of strain energy; (3) avoid the volumetric locking; (4) provides the higher accuracy than those in the node-based smoothed schemes of the original PIMs.

A novel quadratic Edge-based Smoothed Conforming Point Interpolation Method (ES-CPIM) for elasticity problems

his paper formulates an edge-based smoothed conforming point interpolation method (ES-CPIM) for solid mechanics using the triangular background cells. In the ES-CPIM, a technique for obtaining conforming PIM shape functions (CPIM) is used to create a continuous and piecewise quadratic displacement field over the whole problem domain. The smoothed strain field is then obtained through smoothing operation over each smoothing domain associated with edges of the triangular background cells. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. Numerical studies have demonstrated that the ES-CPIM possesses the following good properties: (1) ES-CPIM creates conforming quadratic PIM shape functions, and can always pass the standard patch test; (2) ES-CPIM produces a quadratic displacement field without introducing any additional degrees of freedom; (3) The results of ES-CPIM are generally of very high accuracy.

A hybrid smoothed finite element method (H-SFEM) to solid mechanics problems

In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and Node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained by adjusting ; (2) there exists a preferable at which the H-SFEM can produce the ultrasonic accurate solution.

A coupled SPH/FEM analysis of portable water filled barriers

Portable water filled barriers (PWFB) are semi-rigid roadside barriers which have the potential to display good crash attenuation characteristics at low and moderate impact speeds. The traditional mesh based numerical methods alone fail to simulate this type of impact with precision, stability and efficiency. This paper proposes to develop an advanced simulation model based on the combination of Smoothed Particles Hydrodynamics (SPH), a meshless method, and finite element method (FEM) for fluid-structure analysis using the commercially available software package LS-Dyna. The interaction between SPH particles and FEA elements is studied in this paper. Two methods of element setup at the element boundary were investigated. The response of the impacted barrier and fluid inside were analysed and compared. The system response and lagging were observed and reported in this paper. It was demonstrated that coupled SPH/FEM can be used in full scale PWFB modelling application. This will aid the research in determining the best initial setup to couple FEA and SPH in road safety barrier for impact response and safety analysis in the future.

Fluid-structure interaction analysis of full scale vehicle-barrier impact using coupled SPH-FEA

Portable water-filled barriers (PWFB) are roadside structures used to separate moving traffic from work-zones. Numerical PWFB modelling is preferred in the design stages prior to actual testing. This paper aims to study the fluid-structure interaction of PWFB under vehicular impact using several methods. The strategy to treat water as non-structural mass was proposed and the errors were investigated. It was found that water can be treated with the FEA-NSM model for velocities higher than 80kmh-1. However, full SPH/FEA model is still the best treatment for water and necessary for lower impact velocities. The findings in this paper can be used as guidelines for modelling and designing PWFB.

Porohyperelastic analysis of single osteocyte using AFM and inverse FEA

Osteocytes are the mature cells and perform as mechanosensors within the bone. The mechanical property of osteocytes plays an important role to fulfill these functions. However, little researches have been done to investigate the mechanical deformation properties of single osteocytes. Atomic Force Microscopy (AFM) is a state-of-art experimental facility for high resolution imaging of tissues, cells and any surfaces as well as for probing mechanical properties of the samples both qualitatively and quantitatively. In this paper, the experimental study based on AFM is firstly used to obtain forceindentation curves of single round osteocytes. The porohyperelastic (PHE) model of a single osteocyte is then developed by using the inverse finite element analysis (FEA) to identify and extract mechanical properties from the experiment results. It has been found that the PHE model is a good candidature for biomechanics studies of osteocytes.

Porohyperelastic analysis of single chondrocyte using AFM and inverse FEA

The aim of this paper is to determine the creep and relaxation responses of single chondrocytes in vitro. Firstly, Atomic Force Microscopy (AFM) was used to obtain the force-indentation curves of single chondrocytes at the strain-rate of 7.05 s-1. This result was then employed in inverse finite element analysis (FEA) using porohyperelastic (PHE) idealization of the cells to determine their mechanical properties. The PHE model results agreed well with AFM experimental data. This PHE model was then utilized to study chondrocyte’s creep and relaxation behaviors. The results revealed that the effect of fluid was predominant for cell’s mechanical behaviors and that the PHE is a good model for biomechanics studies of chondrocytes.

A sub‒domain smoothed Galerkin method for solid mechanics problems

A sub‒domain smoothed Galerkin method is proposed to integrate the advantages of mesh‒free Galerkin method and FEM. Arbitrarily shaped sub‒domains are predefined in problems domain with mesh‒free nodes. In each sub‒domain, based on mesh‒free Galerkin weak formulation, the local discrete equation can be obtained by using the moving Kriging interpolation, which is similar to the discretization of the high‒order finite elements. Strain smoothing technique is subsequently applied to the nodal integration of sub‒domain by dividing the sub‒domain into several smoothing cells. Moreover, condensation of DOF can also be introduced into the local discrete equations to improve the computational efficiency. The global governing equations of present method are obtained on the basis of the scheme of FEM by assembling all local discrete equations of the sub‒domains. The mesh‒free properties of Galerkin method are retained in each sub‒domain. Several 2D elastic problems have been solved on the basis of this newly proposed method to validate its computational performance. These numerical examples proved that the newly proposed sub‒domain smoothed Galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency, good accuracy, and convergence.

Experimental and numerical characteristics of portable water-filled road safety barrier system under different impact conditions

This research has developed an innovative road safety barrier system that will enhance roadside safety. In doing so, the research developed new knowledge in the field of road crash mitigation for high speed vehicle impact involving plastic road safety barriers. This road safety barrier system has the required feature to redirecting an errant vehicle with limited lateral displacement. Research was carried out using dynamic computer simulation technique support by experimental testing. Future road safety barrier designers may use the information in this research as a design guideline to improve the performance and redirectional capability of the road safety barrier system. This will lead to better safety conditions on the roadways and potentially save lives.

Smoothed rank-based procedure for censored data

A smoothed rank-based procedure is developed for the accelerated failure time model to overcome computational issues. The proposed estimator is based on an EM-type procedure coupled with the induced smoothing. "The proposed iterative approach converges provided the initial value is based on a consistent estimator, and the limiting covariance matrix can be obtained from a sandwich-type formula. The consistency and asymptotic normality of the proposed estimator are also established. Extensive simulations show that the new estimator is not only computationally less demanding but also more reliable than the other existing estimators.

Standard errors and covariance matrices for smoothed rank estimators

A 'pseudo-Bayesian' interpretation of standard errors yields a natural induced smoothing of statistical estimating functions. When applied to rank estimation, the lack of smoothness which prevents standard error estimation is remedied. Efficiency and robustness are preserved, while the smoothed estimation has excellent computational properties. In particular, convergence of the iterative equation for standard error is fast, and standard error calculation becomes asymptotically a one-step procedure. This property also extends to covariance matrix calculation for rank estimates in multi-parameter problems. Examples, and some simple explanations, are given.

q-Gaussian based Smoothed Functional Algorithms for Stochastic Optimization

The q-Gaussian distribution results from maximizing certain generalizations of Shannon entropy under some constraints. The importance of q-Gaussian distributions stems from the fact that they exhibit power-law behavior, and also generalize Gaussian distributions. In this paper, we propose a Smoothed Functional (SF) scheme for gradient estimation using q-Gaussian distribution, and also propose an algorithm for optimization based on the above scheme. Convergence results of the algorithm are presented. Performance of the proposed algorithm is shown by simulation results on a queuing model.