An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

Tiago, Carlos; Pimenta, Paulo de Mattos

doi:10.1016/j.enganabound.2007.10.014

Cited by 20 publications

(4 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tiago and Pimenta implemented EFG with MLS approximant to nonlinear analysis of plates undergoing arbitrary large deformations which is based on a unified nonlinear theory of plates allowing arbitrarily large rotations and displacements. Presented approach was hybrid in nature where solution was obtained by the independent approximation of the generalized internal displacement fields and generalized boundary tractions [ 61 ]. Hu et al developed MLPG approach for large deformation contact analysis of elastomers like rubber block and compression of rubber ring.…”

Section: Efg and Mlpg: Structure Mechanicsmentioning

confidence: 99%

A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications

Daxini

Prajapati

2014

The Scientific World Journal

View full text Add to dashboard Cite

Meshfree methods are viewed as next generation computational techniques. With evident limitations of conventional grid based methods, like FEM, in dealing with problems of fracture mechanics, large deformation, and simulation of manufacturing processes, meshfree methods have gained much attention by researchers. A number of meshfree methods have been proposed till now for analyzing complex problems in various fields of engineering. Present work attempts to review recent developments and some earlier applications of well-known meshfree methods like EFG and MLPG to various types of structure mechanics and fracture mechanics applications like bending, buckling, free vibration analysis, sensitivity analysis and topology optimization, single and mixed mode crack problems, fatigue crack growth, and dynamic crack analysis and some typical applications like vibration of cracked structures, thermoelastic crack problems, and failure transition in impact problems. Due to complex nature of meshfree shape functions and evaluation of integrals in domain, meshless methods are computationally expensive as compared to conventional mesh based methods. Some improved versions of original meshfree methods and other techniques suggested by researchers to improve computational efficiency of meshfree methods are also reviewed here.

show abstract

Section: Efg and Mlpg: Structure Mechanicsmentioning

confidence: 99%

A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications

Daxini

Prajapati

2014

The Scientific World Journal

View full text Add to dashboard Cite

show abstract

“…To explain this result let us write the discrete bilinear form related to systems (35) and (25) [2]:…”

Section: Lagrange Multipliers Approximation Functionsmentioning

confidence: 99%

“…Most of them are based on strain driven approaches, where the problem's weak form is built either from equilibrium in the domain and on the static boundary or from the potential energy [4,25]. For the same problems, an alternative formulation the so called stress driven approach can also be used.…”

Section: Introductionmentioning

confidence: 99%

Meshless methods in dual analysis: Theoretical and implementation issues

Ivannikov¹,

Tiago²,

Almeida³

et al. 2013

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

a b s t r a c tThis paper presents a meshless implementation of dual analysis for 2D linear elasticity problems. The derivation of the governing systems of equations for the discretized compatible and equilibrated models is detailed and crucial implementation issues of the proposed algorithm are discussed: (i) arising of deficiencies associated with the independent approximation field used for the imposition of the essential boundary conditions (EBC) for the two parts of the boundary sharing a corner and (ii) determination of the Lagrange multipliers functional space used to impose EBC. An attempt to implement the latter resulted in an approximation which is nothing more than the trace on the essential boundary of the domain nodal functions. The difficulties posed by such approximation are explained using the inf sup condition.Several examples of global (energy) and local (displacements) quantities of interest and their bounds determination are used to demonstrate the validity of the presented meshless approach to dual analysis. Numerical assessment of the convergence rates obtained for both models is made, for different poly nomial basis degrees.

show abstract

“…(b) Meshfree methods for contact problems Li et al [154] firstly employed moment matrix of meshfree approximation to formulate a contact detection algorithm, which accurately detected contact for Taylor bar impact problem without solving complex equations. Tiago and Pimenta [155] combined EFG-based meshfree method with MLS approximation to solve the contact problems involving arbitrary large deformations for nonlinear plates. Hu et al [156] studied the large deformation contact of elastomers by using the developed MLPG approach.…”

Section: Meshfree Methodsmentioning

confidence: 99%

Isogeometric analysis-based approaches for fracture and contact problems of structures and materials

Huang¹

View full text Add to dashboard Cite

show abstract

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

Cited by 20 publications

References 40 publications

A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications

A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications

Meshless methods in dual analysis: Theoretical and implementation issues

Isogeometric analysis-based approaches for fracture and contact problems of structures and materials

Contact Info

Product

Resources

About