A finite point method for elasticity problems

Oñate, Eugenio; Perazzo, Franco; Miquel, Juan Carlos

doi:10.1016/s0045-7949(01)00067-0

Cited by 163 publications

(85 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Since the FPM appeared in the literature towards the mid-nineties, it has been successfully applied to solve convective-diffusive problems, incompressible and compressible fluid flow problems [9,10,11,12,13,14] and solid mechanics problems [15,16,17] among others. As regards to fluid flow problems, the first application of the FPM to the solution of the twodimensional compressible flow equations was presented by Oñate et al [8,9] and Fischer [12].…”

Section: The Present Work Deals With a Meshless Technique Called The mentioning

confidence: 99%

“…If the condition number of A is smaller than a given maximum admissible value, and if the calculated shape functions satisfy some quality tests, If matrix P (given by Eq. (4)) has rank m and np m  , it can be uniquely factored as  P QR (15) where matrix Q   np x m is orthogonal ( Q T Q = I ) and matrix R   m x m is upper triangular with positive diagonal elements (a similar procedure, based on columns pivoting, can be applied for cases where matrix P is rank deficient or near rank deficient). In order to apply the QR factorization for solving our WLSQ problem, it is necessary to obtain an equivalent unweighted problem.…”

Section: Numerical Finite Point Approximations On Clouds Of Pointsmentioning

confidence: 99%

See 1 more Smart Citation

A finite point method for adaptive three‐dimensional compressible flow calculations

Ortega

Oñate

Idelsohn

2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

Abstract. The Finite Point Method (FPM) is a meshless technique which is based on both, aWeighted Least-Squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with threedimensional applications concerning real compressible fluid flow problems. In the first part of this work, the upwind biased scheme employed for solving the flow equations is described.

show abstract

Section: The Present Work Deals With a Meshless Technique Called The mentioning

confidence: 99%

Section: Numerical Finite Point Approximations On Clouds Of Pointsmentioning

confidence: 99%

A finite point method for adaptive three‐dimensional compressible flow calculations

Ortega

Oñate

Idelsohn

2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

show abstract

“…There is a vast array of meshfree methods available, as described by Liu et al [26,27]. Some of the more popular meshfree methods are the local radial point interpolation method (LRPIM) [28,29], meshless local Petrov-Galerkin (MLPG) [30], finite point method (FPM) [31], as well as the smoothed particle hydrodynamics method (SPH) [32,33]. Fraser et al [34][35][36][37][38][39][40][41][42][43] have recently developed an advanced meshfree framework on the graphics-processing unit (GPU) to simulate the entire FSW process.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Friction Stir Weld Joint Quality Using a Meshfree Fully-Coupled Thermo-Mechanics Approach

Fraser

Kiss

St-Georges

et al. 2018

Metals

View full text Add to dashboard Cite

Abstract:There is currently a need for an efficient numerical optimization strategy for the quality of friction stir welded (FSW) joints. However, due to the computational complexity of the multi-physics problem, process parameter optimization has been a goal that is out of reach of the current state-of-the-art simulation codes. In this work, we describe an advanced meshfree computational framework that can be used to determine numerically optimized process parameters while minimizing defects in the friction stir weld zone. The simulation code, SPHriction-3D, uses an innovative parallelization strategy on the graphics processing unit (GPU). This approach allows determination of optimal parameters faster than is possible with costly laboratory testing. The meshfree strategy is firstly outlined. Then, a novel metric is proposed that automatically evaluates the presence and severity of defects in the weld zone. Next, the code is validated against a set of experimental results for 1 /2" AA6061-T6 butt joint FSW joints. Finally, the code is used to determine the optimal advancing speed and rpm while minimizing defect volume based on the proposed defect metric.

show abstract

“…Least-squares meshless 2.1. Moving least-squares shape functions Among the available meshless approximation schemes, the Moving Least-Squares (MLS) method [22] is generally considered to be one of the best methods to interpolate random data with a reasonable accuracy due to its completeness, robustness, and continuity [23,24]. With the MLS interpolation, unknown function, (x), is approximated by:…”

Section: Introductionmentioning

confidence: 99%

Optimum two-dimensional crack modeling in discrete least-squares meshless method by charged system search algorithm

2017

View full text Add to dashboard Cite

Abstract. In this paper, a node adaptive rearrangement is presented based on the estimated error in various domains for some problems in the fracture mechanics by Discrete Least-Squares Meshless method (DLSM). This method is one of the approximate methods recently introduced and used in the various elds. The method is based on minimization of the least-squares functional with respect to the nodal parameters, and it uses moving least-squares method for calculating the shape functions. Due to the natural process of problem solving, after calculating the shape functions, the residuals are calculated and their values are considered as an objective function for rearrangement of the nodes. There are three popular methods for constructing shape functions in discontinuous domains, and here, the transparency method is utilized. Similar to other numerical methods, there are di erent procedures for re nement and improvement of the results; however, adaptive rearrangement can be employed without increasing the computational cost. In this paper, the Charged System Search (CSS) algorithm is used as a tool for adaptive rearrangement or repositioning process. E ciency and e ectiveness of the proposed adaptive rearrangement technique is tested by some benchmark two-dimensional crack examples with available analytical solution around crack tips.

show abstract

A finite point method for elasticity problems

Cited by 163 publications

References 22 publications

A finite point method for adaptive three‐dimensional compressible flow calculations

A finite point method for adaptive three‐dimensional compressible flow calculations

Optimization of Friction Stir Weld Joint Quality Using a Meshfree Fully-Coupled Thermo-Mechanics Approach

Optimum two-dimensional crack modeling in discrete least-squares meshless method by charged system search algorithm

Contact Info

Product

Resources

About