scholarly journals Three-dimensional flat shell-to-shell coupling: numerical challenges

2017 ◽  
Vol 4 (1) ◽  
pp. 299-313
Author(s):  
Kuo Guo ◽  
Ghadir Haikal
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Shell Element ◽  
Thin Plates ◽  
Mindlin Plate ◽  
Shell Elements ◽  
Contact Formulation ◽  
Flat Shell ◽  
Surface Contact ◽  
Flat Shell Element

Abstract The node-to-surface formulation is widely used in contact simulations with finite elements because it is relatively easy to implement using different types of element discretizations. This approach, however, has a number of well-known drawbacks, including locking due to over-constraint when this formulation is used as a twopass method. Most studies on the node-to-surface contact formulation, however, have been conducted using solid elements and little has been done to investigate the effectiveness of this approach for beam or shell elements. In this paper we show that locking can also be observed with the node-to-surface contact formulation when applied to plate and flat shell elements even with a singlepass implementation with distinct master/slave designations, which is the standard solution to locking with solid elements. In our study, we use the quadrilateral four node flat shell element for thin (Kirchhoff-Love) plate and thick (Reissner-Mindlin) plate theory, both in their standard forms and with improved formulations such as the linked interpolation [1] and the Discrete Kirchhoff [2] elements for thick and thin plates, respectively. The Lagrange multiplier method is used to enforce the node-to-surface constraints for all elements. The results show clear locking when compared to those obtained using a conforming mesh configuration.

scholarly journals A New Method Applied to the Quadrilateral Membrane Element with Vertex Rigid Rotational Freedom

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Xiaowei Gao ◽  
Yunfei Liu ◽  
Jun Lv
Keyword(s):  
Shell Element ◽  
New Method ◽  
Membrane Element ◽  
Shell Elements ◽  
Local Coordinates ◽  
Flat Shell ◽  
Flat Shell Element ◽  
Cartesian Coordinate ◽  
Derivatives Of ◽  
Rotational Freedom

In order to improve the performance of the membrane element with vertex rigid rotational freedom, a new method to establish the local Cartesian coordinate system and calculate the derivatives of the shape functions with respect to the local coordinates is introduced in this paper. The membrane elements with vertex rigid rotational freedom such as GQ12 and GQ12M based on this new method can achieve higher precision results than traditional methods. The numerical results demonstrate that the elements GQ12 and GQ12M with this new method can provide better membrane elements for flat shell elements. Furthermore, this new method presented in this paper offers a new approach for other membrane elements used in flat shell element to improve the computing accuracy.

scholarly journals Study on the Explicit Formula of the Triangular Flat Shell Element Based on the Analytical Trial Functions for Anisotropy Material

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xiang-Rong Fu ◽  
Li-Na Ge ◽  
Ge Tian ◽  
Ming-Wu Yuan
Keyword(s):  
Analytical Solutions ◽  
High Efficiency ◽  
Shell Element ◽  
High Accuracy ◽  
Triangular Element ◽  
Shell Elements ◽  
Hybrid Element ◽  
Flat Shell ◽  
Flat Shell Element ◽  
Integral Formulae

This paper presents a novel way to formulate the triangular flat shell element. The basic analytical solutions of membrane and bending plate problem for anisotropy material are studied separately. Combining with the conforming displacement along the sides and hybrid element strategy, the triangular flat shell elements based on the analytical trial functions (ATF) for anisotropy material are formulated. By using the explicit integral formulae of the triangular element, the matrices used in proposed shell element are calculated efficiently. The benchmark examples showed the high accuracy and high efficiency.

Thermoviscoelastic analysis of composite structures using a triangular flat shell element

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 238-247
Author(s):  
Daniel C. Hammerand ◽  
Rakesh K. Kapania
Keyword(s):  
Composite Structures ◽  
Shell Element ◽  
Flat Shell ◽  
Flat Shell Element

Fracture Mechanics of Thin Plates and Shells Under Combined Membrane, Bending, and Twisting Loads

2005 ◽  
Vol 58 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Alan T. Zehnder ◽  
Mark J. Viz
Keyword(s):  
Fracture Mechanics ◽  
Plate Theory ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Crack Tip ◽  
Thin Plates ◽  
Element Analysis ◽  
Crack Tip Fields ◽  
Plates And Shells ◽  
Membrane Bending

The fracture mechanics of plates and shells under membrane, bending, twisting, and shearing loads are reviewed, starting with the crack tip fields for plane stress, Kirchhoff, and Reissner theories. The energy release rate for each of these theories is calculated and is used to determine the relation between the Kirchhoff and Reissner theories for thin plates. For thicker plates, this relationship is explored using three-dimensional finite element analysis. The validity of the application of two-dimensional (plate theory) solutions to actual three-dimensional objects is analyzed and discussed. Crack tip fields in plates undergoing large deflection are analyzed using von Ka´rma´n theory. Solutions for cracked shells are discussed as well. A number of computational methods for determining stress intensity factors in plates and shells are discussed. Applications of these computational approaches to aircraft structures are examined. The relatively few experimental studies of fracture in plates under bending and twisting loads are also reviewed. There are 101 references cited in this article.

A Finite Element for the Analysis of Shell Intersections

1996 ◽  
Vol 118 (4) ◽  
pp. 399-406 ◽  
Author(s):  
W. J. Koves ◽  
S. Nair
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Three Dimensional ◽  
Shell Element ◽  
Theory Of Elasticity ◽  
Shell Elements ◽  
Asme Code ◽  
Form Theory ◽  
Computation Scheme ◽  
Shell Intersections

A specialized shell-intersection finite element, which is compatible with adjoining shell elements, has been developed and has the capability of physically representing the complex three-dimensional geometry and stress state at shell intersections (Koves, 1993). The element geometry is a contoured shape that matches a wide variety of practical nozzle configurations used in ASME Code pressure vessel construction, and allows computational rigor. A closed-form theory of elasticity solution was used to compute the stress state and strain energy in the element. The concept of an energy-equivalent nodal displacement and force vector set was then developed to allow complete compatibility with adjoining shell elements and retain the analytical rigor within the element. This methodology provides a powerful and robust computation scheme that maintains the computational efficiency of shell element solutions. The shell-intersection element was then applied to the cylinder-sphere and cylinder-cylinder intersection problems.

A new 3-node triangular flat shell element

2002 ◽  
Vol 18 (3) ◽  
pp. 153-159 ◽  
Author(s):  
J. G. Kim ◽  
J. K. Lee ◽  
Y. K. Park
Keyword(s):  
Shell Element ◽  
Flat Shell ◽  
Flat Shell Element

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
Author(s):  
O. G. McGee ◽  
J. W. Kim ◽  
A. W. Leissa
Keyword(s):  
Plate Theory ◽  
Thin Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Thick Plates ◽  
Thin Plate Theory ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates ◽  
Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

Calculation of Shell Element Failure Based on the State of Stress Inside of a Neck

2015 ◽  
Author(s):  
R. C. Dragt ◽  
J. Kraus ◽  
C. L. Walters
Keyword(s):  
Three Dimensional ◽  
Shell Element ◽  
Offshore Structures ◽  
Shell Elements ◽  
Thin Walled Structures ◽  
Coulomb Failure ◽  
Correct Determination ◽  
Element Failure ◽  
The Relationship

Simulation of failure in thin-walled structures is critical for the correct determination of crash performance of ships and offshore structures. Typically, shell elements are used, but these elements are not able to adequately capture local failure, especially inside of a neck. This paper addresses these gaps by adapting the Bridgman (1952) model of a neck inside of a plate by making it three-dimensional and offering an estimate of the relationship between state parameters of a shell element and the geometry inside of a neck. Finally, recommendations are also made about how to interface this information with the Modified Mohr-Coulomb failure locus to create a practical algorithm for assessing failure in shell elements.

Three-Dimensional Plate Theory for Flexible Multibody Dynamics

2015 ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Flexible Multibody Dynamics ◽  
Composite Plates ◽  
Complex Stress ◽  
Mindlin Plate ◽  
Stress States ◽  
Three Dimensional Elasticity ◽  
Material Line

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

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