Static and dynamic analyses of three-dimensional hollow concrete block revetments using polyhedral finite element method

Nguyen-Ngoc, Hau; Phung‐Van, P.; Dang, Bao-Loi; Nguyen‐Xuan, H.; Wahab, Magd Abdel

doi:10.1016/j.apor.2019.03.012

Cited by 6 publications

(18 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The hollow concrete block is designed as an element of interlocking revetment protecting a dike's slope along an industry zone in Vietnam. 14 shown in Figure 22, which can be used to prove the efficiency of the present method in analyzing complex industrial structures. The wave load, which acts on the front surface, is considered as a distribution load varying from 26 to 28 kPa.…”

Section: D Industrial Complex Hollow Concrete Blockmentioning

confidence: 90%

“…It should be noted that the procedure of solving Galerkin weak form using CIPFEM is similar to conventional FEM. The discretized equivalent equation of solid structures is given by 14,31 :…”

Section: Stiffness Matrix Using Cipfemmentioning

confidence: 99%

“…The polyhedral elements are sub‐divided into sub‐tetrahedra. Consequently, the piecewise linear shape functions over the arbitrary elements with n ne vertices are formulated based on the standard linear shape functions of 4‐node tetrahedral elements 14 :

N_{I}^{normalPL} false(boldx false) = \sum_{J = 1}^{4} ϕ_{J}^{T 4} false(boldx false) N_{I}^{normalPL} false(x_{J} false) for x \in {normalΩ}^{T 4}

{\nabla N}_{I}^{normalPL} false(boldx false) = \sum_{J = 1}^{4} {\nabla ϕ}_{J}^{T 4} false(boldx false) N_{I}^{normalPL} false(x_{J} false) for x \in {normalΩ}^{T 4}

where

N_{I}^{normalPL} false(boldx false)

and

{\nabla N}_{I}^{normalPL} false(boldx false)

are the shape functions and their derivatives of node I ( I = 1: n ne ) at the interpolation point x in sub‐tetrahedron

{normalΩ}^{T 4}

;

ϕ_{J}^{T 4} false(boldx false)

and

{\nabla ϕ}_{J}^{T 4} false(boldx false)

are the standard shape functions and their derivatives of sub‐tetrahedron;

N_{I}^{normalPL} false(x_{J} false)

is the shape function on polyhedron at node x J , which satisfies the Kronecker‐delta property if x J is the vertex of the element, equals to average face's nodes at face's center

…”

Section: A Formulation Based On Cipfemmentioning

confidence: 99%

“…As described in Reference 14, because of using piecewise linear shape function, the accuracy of the PFEM solutions does not depend on the number of Gauss points in each sub‐tetrahedron ( B is a constant matrix with all point of interest

x \in {normalΩ}_{s}

). Nevertheless, CI scheme use high‐order shape functions so that the results can be improved significantly when using higher numbers of quadrature points 28 .…”

Section: A Formulation Based On Cipfemmentioning

confidence: 99%

“…Recently, a new interpolation scheme, the so-called piecewise linear shape function, has been developed for 2D polygonal and 3D polyhedral elements (PFEM), which showed many advantages compared to conventional FEM. 3,14 However, the obtained strain fields are constant over elements' sub-domains due to the nature of the shape functions. Moreover, the gradients between integration elements are discontinuous, which require post processing to smooth the obtained results such as strain, stress over the whole domain.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A consecutive‐interpolation polyhedral finite element method for solid structures

Nguyen

et al. 2021

Numerical Meth Engineering

View full text Add to dashboard Cite

In this paper, we investigate the use of a consecutive-interpolation for polyhedral finite element method (CIPFEM) in the analysis of three-dimensional solid mechanics problems. A displacement-based Galerkin weak form is used, in which the nodal degrees of freedom (DOF) and their derivatives are both considered for the approximation scheme. Based on arbitrary star-convex polyhedral elements using piecewise linear shape function, the present method can have the advantage of being applicable to complicated structures. Nevertheless, the proposed interpolation technique gives higher-order continuity, greater accuracy with the same number of DOFs. The reliability and efficiency of the CIPFEM are proved by comparing the present results with those obtained by the consecutive-interpolation for tetrahedral element (CT4), conventional linear FEM using polyhedral elements (PFEM), and tetrahedral elements (T4) through numerical examples. Cantilever beam, concrete corbel, and complex hollow concrete revetment block are considered to show the excellent performance of the present approach.

show abstract

Section: D Industrial Complex Hollow Concrete Blockmentioning

confidence: 90%

Section: Stiffness Matrix Using Cipfemmentioning

confidence: 99%

N_{I}^{normalPL} false(boldx false) = \sum_{J = 1}^{4} ϕ_{J}^{T 4} false(boldx false) N_{I}^{normalPL} false(x_{J} false) for x \in {normalΩ}^{T 4}

{\nabla N}_{I}^{normalPL} false(boldx false) = \sum_{J = 1}^{4} {\nabla ϕ}_{J}^{T 4} false(boldx false) N_{I}^{normalPL} false(x_{J} false) for x \in {normalΩ}^{T 4}

where

N_{I}^{normalPL} false(boldx false)

and

{\nabla N}_{I}^{normalPL} false(boldx false)

are the shape functions and their derivatives of node I ( I = 1: n ne ) at the interpolation point x in sub‐tetrahedron

{normalΩ}^{T 4}

;

ϕ_{J}^{T 4} false(boldx false)

and

{\nabla ϕ}_{J}^{T 4} false(boldx false)

are the standard shape functions and their derivatives of sub‐tetrahedron;

N_{I}^{normalPL} false(x_{J} false)

is the shape function on polyhedron at node x J , which satisfies the Kronecker‐delta property if x J is the vertex of the element, equals to average face's nodes at face's center

…”

Section: A Formulation Based On Cipfemmentioning

confidence: 99%

x \in {normalΩ}_{s}

). Nevertheless, CI scheme use high‐order shape functions so that the results can be improved significantly when using higher numbers of quadrature points 28 .…”

Section: A Formulation Based On Cipfemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations