Element free analyses of shell and spatial structures

Noguchi, Hirohisa; Kawashima, T.; Miyamura, Tomoshi

doi:10.1002/(sici)1097-0207(20000228)47:6<1215::aid-nme834>3.0.co;2-m

Cited by 119 publications

(41 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The Young's modulus is E = 3.0 × 10 6 ; the Poisson's ratio is ν = 0 and the mass density is ρ = 0.20833. The problem has been analyzed by several researchers using the EFG method, including Krysl and Belytschko [5] and Noguchi et al [17] and using finite Fig. 2 is used to investigate the parameters.…”

Section: Barrel Vault Roofmentioning

confidence: 99%

Conforming radial point interpolation method for spatial shell structures on the stress-resultant shell theory

2006

View full text Add to dashboard Cite

The implementation of the conforming radial point interpolation method (CRPIM) for spatial thick shell structures is presented in this paper. The formulation of the discrete system equations is derived from a stress-resultant geometrically exact theory of shear flexible shells based on the Cosserat surface. A discrete singularity-free mapping between the five degrees of freedom of the Cosserat surface and the normal formulation with six degrees of freedom is constructed by exploiting the geometry connection between the orthogonal group and the unit sphere. A radial basis function is used in both the construction of shape functions based on arbitrarily distributed nodes as well as in the surface approximation of general spatial shell geometries. The major advantage of the CRPIM is that the shape functions possess a delta function property and the interpolation function obtained passes through all the scattered points in the influence domain. Thus, essential boundary conditions can be easily imposed, as in finite element method. A range of shape parameters is studied to examine the performance of CRPIM for shells, and optimal values are proposed. The phenomena of shear locking and membrane locking are illustrated by presenting the membrane and shear energies as fractions of the total energy. Several benchmark problems for shells are analyzed to demonstrate the validity and efficiency of the present CRPIM. The convergence rate of the results using a Gaussian (EXP) radial basis is relatively high compared to those using a multi-quadric (MQ) radial basis for the shell problems.

show abstract

Section: Barrel Vault Roofmentioning

confidence: 99%

Conforming radial point interpolation method for spatial shell structures on the stress-resultant shell theory

2006

View full text Add to dashboard Cite

show abstract

“…However, the shell was developed for small deformations, small strains and elasticity. Three dimensional modelling of shear deformable shells and degenerated shells in a meshfree context was studied by Noguchi et al [2], Li et al [3] and Kim et al [4]. Usually, a low order polynomial basis was used, e.g.…”

Section: Introductionmentioning

confidence: 99%

A meshfree thin shell method for non‐linear dynamic fracture

Rabczuk

Areias

Belytschko

2007

Numerical Meth Engineering

446

135

View full text Add to dashboard Cite

SUMMARYA meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The C 1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto-plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straight forward.

show abstract

“…The function u h (x) is approximated using the surrounding particles using RKPM shape functions. The meshfree method has been shown to be accurate in numerous books and journals [19,20] and for mesh-free analyses of shells as well: [21][22][23][24]. Mesh-free solvers have been evaluated and tested for this particular application [26].…”

Section: Introductionmentioning

confidence: 99%

Interactive Deformation Through Mesh-Free Stress Analysis in Virtual Reality

Faas

Vance

2008

Volume 3: 28th Computers and Information in Engineering Conference, Parts a and B

View full text Add to dashboard Cite

Virtual reality (VR) techniques are used to create an environment that allows an engineer to modify the shape of a part and see the changes in the stress state immediately. A virtual reality application, Interactive Virtual Design Application (IVDA), that allows fast mesh-free analysis of multiple element types, including twodimensional (2D) elements, is described in detail. Taylor series approximations and Pre-conditioned Conjugate Gradient (PCG) methods are used with mesh-free analysis to perform quick reanalysis during interactive shape modification. Prior to this work, only 3D elements were incorporated into the method. The addition of 2D elements greatly expands the potential application of this work. Several software packages including VR Juggler, OpenHaptics, OPCODE, Tahoe and OpenGL/GLM/GLUT libraries are combined in the resulting application to handle a variety of elements. This approach also supports concurrent product design and assembly methods prototyping. The addition of 2D analysis capability is discussed in this paper. The method is described and a sample problem presented. ABSTRACT Virtual reality (VR) techniques are used to create an environment that allows an engineer to modify the shape of a part and see the changes in the stress state immediately. A virtual reality application, Interactive Virtual Design Application (IVDA), that allows fast mesh-free analysis of multiple element types, including two-dimensional (2D) elements, is described in detail. Taylor series approximations and Pre-conditioned Conjugate Gradient (PCG) methods are used with mesh-free analysis to perform quick reanalysis during interactive shape modification. Prior to this work, only 3D elements were incorporated into the method. The addition of 2D elements greatly expands the potential application of this work. Several software packages including VR Juggler, OpenHaptics, OPCODE, Tahoe and OpenGL/GLM/GLUT libraries are combined in the resulting application to handle a variety of elements. This approach also supports concurrent product design and assembly methods prototyping. The addition of 2D analysis capability is discussed in this paper. The method is described and a sample problem presented.

show abstract

Element free analyses of shell and spatial structures

Cited by 119 publications

References 19 publications

Conforming radial point interpolation method for spatial shell structures on the stress-resultant shell theory

Conforming radial point interpolation method for spatial shell structures on the stress-resultant shell theory

A meshfree thin shell method for non‐linear dynamic fracture

Interactive Deformation Through Mesh-Free Stress Analysis in Virtual Reality

Contact Info

Product

Resources

About