THEs-VERSION OF FINITE ELEMENT METHOD FOR LAMINATED COMPOSITES

Fish, Jacob; Guttal, Ravi

doi:10.1002/(sici)1097-0207(19961115)39:21<3641::aid-nme17>3.0.co;2-p

Cited by 54 publications

(11 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The effectiveness of FE techniques relying on mesh superposition has been discussed in the literature for such problems. Examples can be found in [ 42 ], where the

− d −FEM is employed to solve 3D linear elastodynamic problems, and in [ 32 , 35 ] where the s −FEM is employed in the context of multiple model methods.…”

Section: The −Version Of the Finite Element Methodsmentioning

confidence: 99%

“…In the

FEM the solution accuracy is locally enhanced by superposing one or more high−order local meshes onto a global one. This extension of the FEM has been applied successfully for linear static, frequency, and buckling analysis of laminated composite plates and shells [ 31 , 32 , 33 , 34 ], stress analysis of laminated smart structures [ 35 ], microscopic stress analysis of heterogeneous materials [ 36 ], and dynamic crack analysis in steel structures [ 37 ].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of the ps−Version of the Finite Element Method to the Analysis of Laminated Shells

Yan

Vescovini

2023

Materials

View full text Add to dashboard Cite

The development of accurate and efficient numerical methods is of crucial importance for the analysis and design of composite structures. This is even more true in the presence of variable stiffness (VS) configurations, where intricate load paths can be responsible for complex and localized stress profiles. In this work, we present the ps−version of the finite elements method (ps−FEM), a novel FE approach which can perform global/local analysis through different refinement strategies efficiently and easily. Within this framework, the global behavior is captured through a p−refinement by increasing the polynomial order of the elements. For the local one, a mesh−superposition technique, called s−refinement, is used to improve locally the solution by defining a local/fine mesh overlaid to the global/coarse one. The combination of p− and s−refinements enables us to achieve excellent accuracy−to−cost ratios. This paper aims to present the numerical formulation and the implementation aspects of this novel approach to VS composite shell analysis. Numerical tests are reported to illustrate the potential of the method. The results provide a clear insight of its potential to guarantee fast convergence and easy mesh refinement where needed.

show abstract

“…The effectiveness of FE techniques relying on mesh superposition has been discussed in the literature for such problems. Examples can be found in [ 42 ], where the

− d −FEM is employed to solve 3D linear elastodynamic problems, and in [ 32 , 35 ] where the s −FEM is employed in the context of multiple model methods.…”

Section: The −Version Of the Finite Element Methodsmentioning

confidence: 99%

“…In the

Section: Introductionmentioning

confidence: 99%

Application of the ps−Version of the Finite Element Method to the Analysis of Laminated Shells

Yan

Vescovini

2023

Materials

View full text Add to dashboard Cite

show abstract

“…To solve the stiffness equation ( 35) with numerical stability, special care must be taken to avoid the numerical error and singularity. The following triangular factorization scheme is adopted after Fish et al [14][15][16] as well as the conventional diagonal scaling technique. Defining the lower triangular matrix L by the LL T factorization of the stiffness matrix of equation (35) we have…”

Section: Finite-element Mesh Superpositionmentioning

confidence: 99%

“…The idea to overlay arbitrary local mesh on the global mesh was proposed by Belytschko et al [13] recently. Afterwards, Fish et al [14][15][16] accomplished this and proposed the s-version FEM. The s-version FEM is based on the adaptive FEM and error estimation.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical modelling of textile composite materials and structures by the homogenization method

Takano

Uetsuji

Kashiwagi

et al. 1999

Modelling Simul. Mater. Sci. Eng.

View full text Add to dashboard Cite

For the simulation of mechanical behaviours of textile composite materials and structures, a novel hierarchical modelling technique is proposed. Not only the global deformation but also the stresses at multiscales are analysed precisely. Four-level hierarchy is defined for the textile composites such as woven and knitted fabric composites. The stresses at the mesostructure, which is a periodic unit cell of textile composite materials consisting of fibre bundles and matrix, can be evaluated accurately by the homogenization method and finite-element mesh superposition technique. The latter technique makes it possible to overlay arbitrary local fine mesh on the global rough mesh. Anisotropic damage mechanics is also utilized for strength evaluation at the mesoscale. Three-dimensional modelling of the mesostructure of woven and knitted fabric composite materials is shown. Localization analysis has been carried out within practical computational time and cost by the proposed hierarchical modelling.

show abstract

“…Therefore, the finite element mesh superposition method [8] is used together with the homogenization theory to solve the multi-scale problem with both global and local heterogeneity. The mesh superposition method was firstly developed as one of the adaptive FEMs named s-version FEM [21][22][23][24]. In other words, the original mesh superposition method enables us to use a locally refined mesh very easily.…”

Section: Introductionmentioning

confidence: 99%

Multi-scale finite element analysis of porous materials and components by asymptotic homogenization theory and enhanced mesh superposition method

Takano¹,

Zako

Okuno

2003

Modelling Simul. Mater. Sci. Eng.

View full text Add to dashboard Cite

To analyse the macroscopic and microscopic behaviours of heterogeneous materials and components, a multi-scale computational method is studied. Although asymptotic homogenization theory has been the main tool during the last decade to solve various multi-scale problems, the assumption of the periodicity of the microscopic unit cell and the incapability of considering the scale effect have resulted in the limitations to this theory's applications. These problems should be overcome because advanced materials are often used as joint or laminated components and the interface crack problem must be analysed. For this sake, a novel multi-scale finite element method is proposed that uses the enhanced mesh superposition method together with the asymptotic homogenization theory. The finite element mesh superposition method uses the global mesh and the local mesh that is superimposed arbitrarily onto the global mesh. The enhanced method allows the adoption of different constitutive laws for the two meshes. The advantage of the homogenization theory to predict the homogenized material model accurately based on the complex microstructure is still utilized. The homogenized material model is used for the global mesh, whilst the microscopic heterogeneity and the crack are considered in the local mesh with the material properties of the constituents. The formulation, modelling strategy, implementation and numerical accuracy of the proposed method is described. A porous ceramic is studied in the numerical example.

show abstract

THEs-VERSION OF FINITE ELEMENT METHOD FOR LAMINATED COMPOSITES

Cited by 54 publications

References 22 publications

Application of the ps−Version of the Finite Element Method to the Analysis of Laminated Shells

Application of the ps−Version of the Finite Element Method to the Analysis of Laminated Shells

Hierarchical modelling of textile composite materials and structures by the homogenization method

Multi-scale finite element analysis of porous materials and components by asymptotic homogenization theory and enhanced mesh superposition method

Contact Info

Product

Resources

About