The MITC4+ shell element and its performance

Ko, Yeongbin,Lee, Phill-Seung,Bathe, Klaus-Jü,rgen Elsevier 2016 Computers & structures Vol.169 No.-

<P><B>Abstract</B></P> <P>The objective in this paper is to improve the performance of the 4-node MITC quadrilateral shell finite element, referred to as the MITC4 element (Dvorkin and Bathe, 1984). We propose a new MITC4 shell element, the MITC4+ element, in which the mid-surface membrane strain components are assumed using the concept of the MITC method. The tying membrane strains are obtained from four triangular domains which subdivide the mid-surface of the 4-node quadrilateral shell element. This approach alleviates locking that can happen when the MITC4 shell elements are geometrically distorted in curved geometries. Several basic tests including the isotropy, zero energy mode, and patch tests are performed. Through the solution of various shell problems, the convergence behavior of the MITC4+ shell element is studied to show the improvements reached.</P> <P><B>Highlights</B></P> <P> <UL> <LI> An effective new 4-node shell element is derived from the MITC4 shell element. </LI> <LI> A new assumed membrane strain field is developed to alleviate membrane locking. </LI> <LI> The numerical results show the improved predictive capability. </LI> </UL> </P>

Defect-free 4-node flat shell element: NMS-4F element

Choi, Chang-Koon,Lee, Phill-Seung,Park, Yong-Myung Techno-Press 1999 Structural Engineering and Mechanics, An Int'l Jou Vol.8 No.2

A versatile 4-node shell element which is useful for the analysis of arbitrary shell structures is presented. The element is developed by flat shell approach, i.e., by combining a membrane element with a Mindlin plate element. The proposed element has six degrees of freedom per node and permits an easy connection to other types of finite elements. In the plate bending part, an improved Mindlin plate has been established by the combined use of the addition of non-conforming displacement modes (N) and the substitute shear strain fields (S). In the membrane part, the nonconforming displacement modes are also added to the displacement fields to improve the behavior of membrane element with drilling degrees of freedom and the modified numerical integration (M) is used to overcome the membrane locking problem. Thus the element is designated as NMS-4F. The rigid link correction technique is adopted to consider the effect of out-of-plane warping. The shell element proposed herein passes the patch tests, does not show any spurious mechanism and does not produce shear and membrane locking phenomena. It is shown that the element produces reliable solutions even for the distorted meshes through the analysis of benchmark problems.

The use of the strain approach to develop a new consistent triangular thin flat shell finite element with drilling rotation

Guenfoud, Hamza,Himeur, Mohamed,Ziou, Hassina,Guenfoud, Mohamed 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.68 No.4

In the present paper, we offer a new flat shell finite element. It is the result of the combination of a membrane element and a bending element, both based on the strain-based formulation. It is known that $C^{\circ}$ plane membrane elements provide poor deflection and stress for problems where bending is dominant. In addition, they encounter continuity and compliance problems when they connect to C1 class plate elements. The reach of the present work is to surmount these problems when a membrane element is coupled with a thin plate element in order to construct a shell element. The membrane element used is a triangular element with four nodes, three nodes at the vertices of the triangle and the fourth one at its barycenter. Each node has three degrees of freedom, two translations and one rotation around the normal. The coefficients related to the degrees of freedom at the internal node are subsequently removed from the element stiffness matrix by using the static condensation technique. The interpolation functions of strain, displacements and stresses fields are developed from equilibrium conditions. The plate element used for the construction of the present shell element is a triangular four-node thin plate element based on Kirchhoff plate theory, the strain approach, the four fictitious node, the static condensation and the analytic integration. The shell element result of this combination is robust, competitive and efficient.

An element-based 9-node resultant shell element for large deformation analysis of laminated composite plates and shells

Han, S.C.,Kim, K.D.,Kanok-Nukulchai, W. Techno-Press 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.18 No.6

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

The use of the strain approach to develop a new consistent triangular thin flat shell finite element with drilling rotation

Hamza Guenfoud,Mohamed Himeur,Hassina Ziou,Mohamed Guenfoud 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.68 No.4

In the present paper, we offer a new flat shell finite element. It is the result of the combination of a membrane element and a bending element, both based on the strain-based formulation. It is known that C° plane membrane elements provide poor deflection and stress for problems where bending is dominant. In addition, they encounter continuity and compliance problems when they connect to C1 class plate elements. The reach of the present work is to surmount these problems when a membrane element is coupled with a thin plate element in order to construct a shell element. The membrane element used is a triangular element with four nodes, three nodes at the vertices of the triangle and the fourth one at its barycenter. Each node has three degrees of freedom, two translations and one rotation around the normal. The coefficients related to the degrees of freedom at the internal node are subsequently removed from the element stiffness matrix by using the static condensation technique. The interpolation functions of strain, displacements and stresses fields are developed from equilibrium conditions. The plate element used for the construction of the present shell element is a triangular four-node thin plate element based on Kirchhoff plate theory, the strain approach, the four fictitious node, the static condensation and the analytic integration. The shell element result of this combination is robust, competitive and efficient.

An interface shell element for coupling non-matching quadrilateral shell meshes

Ho-Nguyen-Tan, Thuan,Kim, Hyun-Gyu Elsevier 2018 Computers & structures Vol.208 No.-

<P><B>Abstract</B></P> <P>In this study, a novel interface shell element (ISE) is developed based on a variable-node element formulation to couple non-matching quadrilateral shell meshes. Shape functions for ISEs are explicitly presented in a polynomial form with the use of appropriate supports of weight functions in moving least square (MLS) approximation. Assumed natural strains in the form of the mixed interpolation of tensorial components (MITC) approach are employed to avoid the transverse shear locking when the thickness of shell tends to zero. Moreover, an assumed membrane strain field defined over quadrilateral subdomains subdividing an ISE is used to alleviate the membrane locking in curved ISEs. Numerical experiments show the effectiveness and efficiency of ISE for connecting dissimilar quadrilateral shell meshes at a common interface.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Interface shell elements can be easily defined to couple non-matching quadrilateral shell meshes. </LI> <LI> Shape functions for interface shell elements are explicitly presented in a polynomial form. </LI> <LI> The MITC approach is successfully employed to avoid the transverse shear locking of interface shell elements. </LI> <LI> An assumed membrane strain field is used to alleviate the membrane locking in curved interface shell elements. </LI> <LI> Interface shell elements can successfully alleviate locking phenomena and show good convergence for non-matching mesh problems. </LI> </UL> </P>

활절로 지지된 원통형 적층복합쉘의 기하학적 비선형 해석

한성천 ( Sung Cheon Han ) 한국복합신소재구조학회 2012 복합신소재학회논문집 Vol.3 No.2

In the present study, an Element-Based Lagrangian Formulation for the nonlinear analysis of shell structures is presented. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The Element-Based Lagrangian Formulation of a 9-node resultant- stress shell element is presented for the anisotropic composite material. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Numerical examples for laminated composite curved shells presented herein clearly show the validity of the present approach and the accuracy of the developed shell element.

A new 4-node MITC element for analysis of two-dimensional solids and its formulation in a shell element

Ko, Y.,Lee, P.S.,Bathe, K.J. Pergamon Press ; Elsevier Science Ltd 2017 Computers & structures Vol.192 No.-

We present in this paper a new reliable and efficient 4-node quadrilateral element, which we call the 2D-MITC4 element, for two-dimensional plane stress and plane strain solutions of solids using the MITC method. We also present an extension of the element assuming a constant element pressure, which we call the 2D-MITC4/1 element. The elements show a much better predictive capability than the displacement-based element and perform in linear analyses almost as well as the 4-node element with incompatible modes, an enhanced assumed strain (EAS) element. However, unlike when using EAS elements, we do not observe spurious instabilities in geometrically nonlinear solutions. Embedding the new MITC formulation into the previously presented MITC4+ shell element, we improve the membrane behavior of the shell element. The new 2D solid elements and the improved MITC4+ shell element pass all basic tests (the isotropy, zero energy mode and patch tests). We present the finite element solutions of various benchmark problems to illustrate the solution accuracy of the new elements.

3차원 솔리드-평면 쉘 변환요소의 강성행렬 추정

정성진(Jung, Sung-Jin),이민섭(Lee, Min-Sub) 대한건축학회 2014 大韓建築學會論文集 : 構造系 Vol.30 No.7

A structural model consists of many types of finite elements, such as truss, beam, plate, shell and solid element, and so on. With the aid of commercial computer programs, field engineers comfortably use these finite elements at the same time for the modelling and analysis of real structure in their new projects. However, it is still difficult to model the connections and interfaces between different types of finite elements because of mutually ill-matched node numbers and degrees of freedom(d.o.f). To settle these problems, Many researchers studied and proposed various solution methods in literatures on FEA(Finite Element Analysis) and the use of transition elements is considered as one of the solutions. This pater presents an isoparametric formulation for three dimensional transition finite element, especially the solid-flat shell transition element. The proposed solid-flat shell transition element is composed of the solid element with 8 nodes, 3 d.o.f and the flat shell element with 4 nodes, 6 d.o.f for the simple formula derivation and the usefulness of practical applications. Basic theories for solid element and flat shell element are studied at first and a possible method for realizing the solid-flat shell transition element is suggested. On the basis of these theoretical backgrounds, the formula which calculates the stiffness matrix of the solid-flat shell transition element is derived in detail and an algorithm available for computer programming is investigated lastly.

Explicit Simulation of Roll Forming Process with EAS Solid-shell Elements

L.M. Lia,Y.H. Peng,D.Y. Li 한국소성가공학회 2010 기타자료 Vol.2010 No.6

Solid-shell elements can be seen as a class of typical double-surface shell elements with no rational degrees of freedom, which are more suitable for analyzing double-sided contact problems than conventional shell elements. In this study, an EAS-based solid-shell element is implemented into the explicit finite element formulation to simulate roll forming process. A twelve-parameter enhanced assumed strain (EAS) method is adopted to solve for the locking pathologies. Accuracy of the explicit solid-shell finite element model is excised through two NUMISHEET benchmark tests. Afterwards, a U-channel forming is simulated with the present explicit model. Numerical results of longitudinal strains and final geometries are compared with experiment as well as calculated by the commercial software ABAQUS. The solid-shell element is found more applicable in dealing with roll-forming process than ABAQUS inherent elements. Potential of the explicit solid-shell model in analyzing cold roll forming process is confirmed.