Stochastic meshfree method for elasto-plastic damage analysis

Arun, C. O.; Rao, B. N.; Srinivasan, Sivakumar M.

doi:10.1016/j.cma.2010.04.009

Cited by 26 publications

(7 citation statements)

References 42 publications

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“…Since an explicit formulation is not available for above random field, discretization of it in selected domain is opted for the proposed methodology. 23,24 In the present work, each subdomain is discretized in to 1000 numbers of spatially distributed points, named as nodal points, with associated random variables and shape function method based on MLS approximation is used to reproduce random field and meshless shape function method can be used for approximating the random field over these spatially discretized points. 23,24 Meshless methods are widely used for displacement approximation in solving governing differential equations without discretizing domains into elements.…”

Section: Modelling Of Initial Work Surfacementioning

confidence: 99%

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Feed based trajectory addition and elimination algorithm combined with stochastic meshless modelling to simulate roughness in surface grinding

Sooraj

Arun

Jithendrakumar

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part E:

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Surface grinding is observed to be an inevitable machining event in many of the functional engineering surfaces after pre-processing stages such as milling. Prediction of roughness profile after grinding on such initial surfaces, for selected operating conditions and grinding wheel specification, is always an interesting topic of investigation. Though a number of models have been reported in prior art, value additions through hybrid modelling strategies have been always contributing positively to this field of research due to the stochastic nature of abrasive interactions. Since feed rate of work piece is identified as a key grinding variable influencing the surface roughness, present paper introduces grain trajectory addition and elimination algorithm driven by feed based time scale to predict the ground surface topography. A realistic initial surface modelling is considered using meshless moving least square approximation incorporating both roughness as well as geometric deviation, expected to be imparted during pre-grinding stages. The algorithm is configured to compute two dimensional roughness parameters from the simulated surface profiles and these results are compared with experimental outcomes at various depths of grinding to validate the proposed model.

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Section: Modelling Of Initial Work Surfacementioning

confidence: 99%

“…This method is also been effectively used for random field modelling. 23,24 Based on this, the field can be represented as;…”

Section: Modelling Of Initial Work Surfacementioning

confidence: 99%

Feed based trajectory addition and elimination algorithm combined with stochastic meshless modelling to simulate roughness in surface grinding

Sooraj

Arun

Jithendrakumar

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part E:

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show abstract

“…For example, Rahman and Rao (2001) extended the element-free Galerkin method to develop a stochastic meshless method for the linear elasticity problem. Arun et al (2010) combined Karhunen-Loève expansion with an element-free Galerkin method for the elastoplastic problem. Kim and Inoue (2004) developed the spectral stochastic element-free Galerkin method adopting Karhunen-Loève expansion and Polynomial Chaos series for the linear elastic problems involving random material properties.…”

Section: Introductionmentioning

confidence: 99%

Perturbation based stochastic isogeometric analysis for bending of functionally graded plates with the randomness of elastic modulus

Nguyen

2020

Lat. Am. j. solids struct.

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We propose, in this paper, stochastic isogeometric analysis (SIGA) is a type of non-statistic approach in which combines the perturbation technique with the standard isogeometric analysis, in particular for static behavior of functionally graded plates with the uncertain elastic modulus. We assume that the spatial random variation of elastic modulus can be modeled as a two dimensional Gaussian random field in the plane of the plate. The random field is discretized to set of random variables using the integration point method. The system equations of SIGA are created using the NURBS functions for approximation displacement fields in conjunction with the first-order and second-order perturbation expansions of random fields, stiffness matrix, displacement fields. Besides the non-statistic approach, Monte Carlo simulation is presented for validation. The accuracy and appropriateness of the non-statistic approach are demonstrated via comparisons of the present results with those given by the stochastic finite element method in the literature and by the Monte Carlo analysis as well. The numerical examples are employed to investigate the effect of the randomness of elastic modulus and system parameters on the first and second statistical moments of displacement.

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“…A stochastic meshfree method for the solving of boundaryvalue problems in damage mechanics was presented under elastoplastic conditions; isotropic ductile damage evolution law is used to model the coupled elastoplastic damage growth [44].…”

Section: Introductionmentioning

confidence: 99%