Use of higher-order Legendre polynomials for multilayered plate elements with node-dependent kinematics

2018 ◽  
Vol 202 ◽  
pp. 222-232 ◽  
Author(s):  
E. Zappino ◽  
G. Li ◽  
A. Pagani ◽  
E. Carrera ◽  
A.G. de Miguel
Keyword(s):  
Legendre Polynomials ◽  
Higher Order ◽  
Multilayered Plate ◽  
Plate Elements

LEFM Analysis of V-Notched Aluminum Plates Using Higher-Order Layerwise Model

2014 ◽  
Vol 898 ◽  
pp. 355-358
Author(s):  
Kwang Sung Woo ◽  
Yoo Mi Kwon ◽  
Dong Woo Lee ◽  
Hee Joong Kim
Keyword(s):  
Legendre Polynomials ◽  
Present Method ◽  
Higher Order ◽  
Virtual Crack Closure Technique ◽  
Shape Functions ◽  
Intensity Factors ◽  
Displacement Fields ◽  
Closure Technique ◽  
Aluminum Plates ◽  
Convergent Approach

Higher-order layerwise model is proposed to determine stress intensity factors using virtual crack closure technique for V-notched plates. Present method is based on p-convergent approach and adopts the concept of subparametric element. In assumed displacement field, strain-displacement relations and 3-D constitutive equations of a layer are obtained by combination of 2-D and 1-D higher-order shape functions. Thus, it allows independent implementation of p-refinement for in-plane and transversal displacements. In the proposed elements, the integrals of Legendre polynomials and Gauss-Lobatto technique are employed to interpolate displacement fields and to implement numerical quadrature, respectively.

Higher-Order Theories for Structural Analysis Using Legendre Polynomial Expansions

1969 ◽  
Vol 36 (4) ◽  
pp. 757-762 ◽  
Author(s):  
A. I. Soler
Keyword(s):  
Structural Analysis ◽  
Legendre Polynomials ◽  
Direct Reduction ◽  
Beam Theory ◽  
Plane Elasticity ◽  
Higher Order ◽  
Governing Equations ◽  
Field Equations ◽  
Displacement Boundary ◽  
Polynomial Expansions

Governing equations of plane elasticity are examined to define suitable approximate theories. Each dependent variable in the problem is considered as a series expansion in Legendre polynomials; attention is focused on establishment of a logical approach to truncation of the series. Important variables for approximate theories of any order are established from energy considerations, and the desired approximate theories are established by direct reduction of the field equations and also from an energy viewpoint. A new “classical” beam theory is developed capable of treating displacement boundary conditions on lateral surfaces. Higher-order approximate theories are studied to make certain comparisons with exact solutions; the results of these comparisons indicate that the new method yields approximate theories which may be more accurate than previous theories with similar levels of approximation.

Higher-Order Plate Elements for Large Deformation Analysis in Multibody Applications

2016 ◽  
Author(s):  
Henrik Ebel ◽  
Marko K. Matikainen ◽  
Vesa-Ville Hurskainen ◽  
Aki Mikkola
Keyword(s):  
Large Deformation ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Higher Order ◽  
Deformation Analysis ◽  
Numerical Convergence ◽  
Plate Elements ◽  
Negative Effect ◽  
Numerical Performance ◽  
Locking Phenomena

This study introduces higher-order three-dimensional plate elements based on the absolute nodal coordinate formulation (ANCF) for large deformation multibody applications. The introduced elements employ four to eight nodes and the St. Venant-Kirchhoff material law. A newly proposed eight-node element is carefully verified using various numerical experiments intended to discover possible locking phenomena. In the introduced plate elements, the usage of polynomial approximations of second order in all three directions is found to be advantageous in terms of numerical performance. A comparison of the proposed eight-node element to the introduced four-node higher-order plate elements reveals that the usage of in-plane slopes as nodal degrees of freedom has a negative effect on numerical convergence properties in thin-plate use-cases.

Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures

2018 ◽  
Vol 22 (7) ◽  
pp. 2302-2329
Author(s):  
Lan T That-Hoang ◽  
Hieu Nguyen-Van ◽  
Thanh Chau-Dinh ◽  
Chau Huynh-Van
Keyword(s):  
Nonlinear Analysis ◽  
Shear Deformation ◽  
Composite Structures ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Numerical Results ◽  
Quadrilateral Plate ◽  
Plate Elements ◽  
Strain Smoothing

This paper improves four-node quadrilateral plate elements by using cell-based strain smoothing enhancement and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of composite structures. Small strain-large displacement theory of von Kármán is used in nonlinear formulations of four-node quadrilateral plate elements that have strain components smoothed or averaged over the sub-domains of the elements. From the divergence theory, the displacement gradients in the smoothed strains are transformed from the area integral into the line one. The behavior of composite structures follows the third-order shear deformation theory. The solution of the nonlinear equilibrium equations is obtained by the iterative method of Newton–Raphson with the appropriate convergence criteria. The present numerical results are compared with the other numerical results available in the literature in order to demonstrate the effectiveness of the developed element. These results also contribute a better knowledge and understanding of nonlinear bending behaviors of these composite structures.

Sign in / Sign up

Export Citation Format

Share Document