Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

This paper presents an elasto-plastic element free Galerkin formulation based on Newton-Raphson algorithm for damage growth analysis. Isotropic ductile damage evolution law is used. A study has been carried out in this paper using the proposed element free Galerkin method to understand the effect of initial damage and its growth on structural response of single and bi-material problems. Asimple method is adopted for enforcing EBCs by scaling the function approximation using a scaling matrix, when non-singular weight functions are used over the entire domain of the problem definition. Numerical examples comprising of oneand two-dimensional problems are presented to illustrate the effectiveness of the proposed method in analysis of uniform and non-uniform damage evolution problems. Effect of material discontinuity on damage growth analysis is also presented. © 2010 Indian Academy of Sciences.

Department of Civil Engineering

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Sadhana - Academy Proceedings in Engineering Sciences

Continuum damage growth analysis using element free Galerkin method

This paper presents a stochastic meshfree method for solving boundary. -value problems in damage mechanics under elasto. -plastic conditions. Isotropic ductile damage evolution law is used to model the coupled elasto. -plastic damage growth. Uncertainty associated with initial damage in materials is considered as random field. Moving least squares shape function method and Karhunen Loève expansion method are used for random field discretization. Statistical parameters of the response quantities are computed using perturbation method. The proposed method involves a new stochastic stress update procedure to solve the nonlinear equations in terms of discretized random variables arising from perturbation of equilibrium equations system. Numerical examples comprising of one and two dimensional problems are presented to illustrate the effectiveness of proposed method. © 2010 Elsevier B.V.

Computer Methods in Applied Mechanics and Engineering

Stochastic meshfree method for elasto-plastic damage analysis

This paper presents two formulations for material discontinuity modeling in the element-free Galerkin method. The proposed methods involve an element-free Galerkin formulation in conjunction with two types of transformation methods which relate the nodal parameters and their corresponding physical nodal values to treat the material discontinuities in elastic bi-materials. The proposed methods eliminate the shortcomings of existing methods like Lagrange multiplier method, discontinuity enrichment method and penalty method typically used for material discontinuity treatment in element-free Galerkin formulations. Numerical examples show that the proposed methods yield accurate estimates of solutions.

Journal of Structural Engineering (Madras)

On material discontinuity modeling in element free Galerkin method

In the stochastic mechanics community, the need to account for uncertainty has long been recognized as key to achieving the reliable design of structural and mechanical systems. It is generally agreed that advanced computational tools must be employed to provide the necessary computational framework for describing structural response. A currently popular method is the stochastic finite element method (SFEM), which integrates probability theory with the standard finite element method (FEM). However, SFEM requires a structured mesh to perform the underlying finite element analysis. It is generally recognized that the creation of workable meshes for complex geometric configurations can be difficult, time consuming, and expensive. This discrepancy is further exacerbated when solving solid mechanics problems characterized by a continuous change in the geometry of the domain under analysis. The underlying structures of these methods, which rely on a mesh, are cumbersome in treating moving cracks or mesh distortion. Consequently, the only viable option when applying FEM is to remesh during each discrete step of the model's evolution. This creates numerical difficulties, even for deterministic analysis, and often leads to degradation in solution accuracy, complexity in computer programming, and a computationally intensive environment. Consequently, there is considerable interest in eliminating or greatly simplifying the meshing task. In recent years, a class of Galerkin-based meshfree or meshless methods have been developed that do not require a structured mesh to discretize the problem, such as the element-free Galerkin method, and the reproducing kernel particle method. These methods employ a moving least-squares approximation method that allows resultant shape functions to be constructed entirely in terms of arbitrarily placed nodes. Meshless discretization presents significant advantages for modeling fracture propagation. By sidestepping remeshing requirements, crack-propagation analysis can be dramatically simplified. Since mesh generation of complex structures can be far more time-consuming and costly than the solution of a discrete set of linear equations, the meshless method provides an attractive alternative to FEM. However, most of the development in meshless methods to date has focused on deterministic problems. Research into probabilistic meshless analysis has not been widespread and is only now gaining attention. Due to inherent uncertainties in loads, material properties and geometry, a probabilistic meshless model is ultimately necessary. Hence, there is considerable interest in developing stochastic meshless methods capable of addressing uncertainties in loads, material properties and geometry, and of predicting the probabilistic response of structures. This paper presents a new stochastic meshless method for predicting probabilistic structural response of cracked structures i.e., mean and variance of the fracture parameters. Copyright © 2007 by ASME.

American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP

Stochastic meshfree method for computational fracture mechanics

A stochastic meshless method is presented for solving boundary-value problems in damage mechanics under elastic-plastic conditions that involves random material properties. Material is assumed to have an initial damage, which follows a lognormal filed. An isotropic unified damage law, formulated by Lemaitre is used in this study. A meshless formulation based on element free Galerkin method (EFGM) is developed to predict stochastic structural response. A scaled matrix approach is used for applying the essential boundary conditions in EFGM. The proposed method is based on perturbation technique. First order perturbation technique for damage growth in an elastic plastic analysis is formulated. Newton-Raphson algorithm is used to solve for material nonlinearity. A numerical example is solved to study the effect of random initial damage in the structural response and further damage growth. Monte Carlo technique is used to validate the proposed method. © 2008 by ASME.

Stochastic damage growth analysis using EFGM

A stochastic meshless method is presented for solving boundary-value problems in damage mechanics under linear elastic conditions that involves random material properties. The material properties are formulated as a function of isotropic damage and damage is modeled as a homogeneous random field. A meshless formulation is developed to predict stochastic structural response. Unlike the finite element method, the meshless method requires no structured mesh, since only a scattered set of nodal points is required in the domain of interest. There is no need for fixed connectivities between nodes. In conjunction with the meshless equations, classical perturbation expansions are derived to predict second-moment characteristics of response. Numerical examples based on one- and two-dimensional problems are presented to examine the accuracy and convergence of the stochastic meshless method. A good agreement is obtained between the results of the proposed method and Monte Carlo simulation. Since mesh generation of complex structures can be a far more time-consuming and costly effort than the solution of a discrete set of equations, the meshless method provides an attractive alternative to finite element method for solving stochastic mechanics problems.

A stochastic meshless method for damage mechanics

Computational Mechanics

An application of stochastic meshfree method in the field of fracture mechanics

Deterioration of reinforced concrete structures is a widespread problem all over the world Chloride induced corrosion is one of the major causes of time dependent deterioration of reinforced concrete structures. This paper presents a method for the assessment of time dependent reliability of reinforced concrete beams damaged by chloride induced reinforcement corrosion.Reliability is estimated using first order second moment method and Monte-Carlo simulation technique. Serviceability limit state with respect to corrosion based cracks and limit state of flexure and shear are considered. Also the effect of cover on the reliability with respect to corrosion is studied.