scholarly journals Robustness of Hierarchical Laminated Shell Element Based on Equivalent Single-Layer Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Jae S. Ahn ◽  
Seung H. Yang ◽  
Kwang S. Woo
Keyword(s):  
Three Dimensional ◽  
Single Layer ◽  
Laminated Composite ◽  
Shell Element ◽  
Linear Mapping ◽  
Large Radius ◽  
Laminated Shell ◽  
Shell Elements ◽  
Aspect Ratios ◽  
Material Conditions

This paper deals with the hierarchical laminated shell elements with nonsensitivity to adverse conditions for linear static analysis of cylindrical problems. Displacement approximation of the elements is established by high-order shape functions using the integrals of Legendre polynomials to ensureC0continuity at the interface between adjacent elements. For exact linear mapping of cylindrical shell problems, cylindrical coordinate is adopted. To find global response of laminated composite shells, equivalent single-layer theory is also considered. Thus, the proposed elements are formulated by the dimensional reduction from three-dimensional solid to two-dimensional plane which allows the first-order shear deformation and considers anisotropy due to fiber orientation. The sensitivity tests are implemented to show robustness of the present elements with respect to severe element distortions, very high aspect ratios of elements, and very large radius-to-thickness ratios of shells. In addition, this element has investigated whether material conditions such as isotropic and orthotropic properties may affect the accuracy as the element distortion ratio is increased. The robustness of present element has been compared with that of several shell elements available in ANSYS program.

scholarly journals ESL Based Cylindrical Shell Elements with Hierarchical Shape Functions for Laminated Composite Shells

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Jae S. Ahn ◽  
Seung H. Yang ◽  
Kwang S. Woo
Keyword(s):  
Cylindrical Shell ◽  
Three Dimensional ◽  
Single Layer ◽  
Laminated Composite ◽  
Shell Element ◽  
Composite Shells ◽  
Shell Elements ◽  
Cylindrical Coordinate ◽  
Laminated Composite Shells ◽  
Geometry Mapping

We introduce higher-order cylindrical shell element based on ESL (equivalent single-layer) theory for the analysis of laminated composite shells. The proposed elements are formulated by the dimensional reduction technique from three-dimensional solid to two-dimensional cylindrical surface with plane stress assumption. It allows the first-order shear deformation and considers anisotropic materials due to fiber orientation. The element displacement approximation is established by the integrals of Legendre polynomials with hierarchical concept to ensure theC0-continuity at the interface between adjacent elements as well asC1-continuity at the interface between adjacent layers. For geometry mapping, cylindrical coordinate is adopted to implement the exact mapping of curved shell configuration with a constant curvature with respect to any direction in the plane. The verification and characteristics of the proposed element are investigated through the analyses of three cylindrical shell problems with different shapes, loadings, and boundary conditions.

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.

Free Vibration of Skew Laminates – A Brief Review and Some Benchmark Results

2019 ◽  
Vol 161 (A4) ◽  
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Composite Laminates ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Static And Dynamic Analysis ◽  
Aspect Ratios ◽  
Skew Angles

This study investigates and reviews prior research works on skew composite laminates. The equivalent single layer theories are explored and discussed. An exhaustive review on static and dynamic analysis of composite skew laminates is also presented. Subsequently, a nine node isoparametric plate bending element is used for free vibration analysis of laminated composite skew plate with central skew cut out. The effect of shear deformation is incorporated in the formulation considering first order shear deformation theory. Two types of mass lumping schemes are analysed to study the effect of rotary inertia. Certain numerical examples of plates having different skew angles, skew cut out sizes, boundary conditions, thickness ratios (h/a), aspect ratios (a/b), fiber orientations and number of layers are solved which will be useful for benchmarking of future studies.

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.

A FINITE ELEMENT PLATE FORMULATION FOR THE ACOUSTICAL INVESTIGATION OF THIN AIR LAYERS

2013 ◽  
Vol 21 (04) ◽  
pp. 1350014 ◽  
Author(s):  
PING RONG ◽  
OTTO VON ESTORFF ◽  
LORIS NAGLER ◽  
MARTIN SCHANZ
Keyword(s):  
Finite Element ◽  
Power Series ◽  
Transmission Loss ◽  
Fluid Layer ◽  
Single Layer ◽  
Shell Element ◽  
Thin Plates ◽  
Element Analysis ◽  
Shell Elements ◽  
Double Wall

Double wall systems consisting of thin plates separated by an air gap are common light-weighted wall structures with high transmission loss. Generally, these plate-like structures are modeled in a finite element analysis with shell elements and volume elements for the air (fluid) layer. An alternative approach is presented in this paper, using shell elements for the air layer as well. First, the element stiffness matrix is obtained by removing the thickness dependence of the variational form of the Helmholtz equation by use of a power series. Second, the coupling between the acoustical shell element and the elastic structure is described. To verify the new shell element, a simple double wall system is considered. Comparing the predicted sound field with the results from a commercial FE software (with a single layer of volume elements) a very good agreement is observed. At the same time, employing the new elements with a third-order power series (4 DOFs per node), the calculation time is reduced.

Isogeometric nonlinear shell elements for thin laminated composites based on analytical thickness integration

2016 ◽  
Vol 01 (03n04) ◽  
pp. 1640010 ◽  
Author(s):  
Farshad Roohbakhshan ◽  
Roger A. Sauer
Keyword(s):  
Composite Shell ◽  
Plate Theory ◽  
Single Layer ◽  
Laminated Composite ◽  
Material Model ◽  
Material Behavior ◽  
Large Strains ◽  
Shell Elements ◽  
Shell Models ◽  
Laminated Composite Shells

This paper presents two different formulations for the modeling of thin laminated composite shells, which do not need any numerical integration through the shell thickness. The two proposed formulations are suitable for thin rotation-free shells based on Kirchhoff–Love kinematics. The composite shell is modeled in the framework of equivalent single layer (ESL) theory and the kinematics are adopted from classical laminated plate theory. The two formulations allow for any desired nonlinear isotropic or anisotropic material model as well as arbitrary large strains and deformations. The presented shell models can be used to analyze any arrangement and material behavior of the laminate layers. The FE solution is based on isogeometric analysis (IGA). Quadratic NURBS-based elements are used to ensure the smoothness required for the analysis of thin shells. The robustness and accuracy of the formulation is demonstrated by various numerical examples.

FREE VIBRATION OF SKEW LAMINATES – A BRIEF REVIEW AND SOME BENCHMARK RESULTS

2021 ◽  
Vol 161 (A4) ◽  
Author(s):  
S Haldar ◽  
S Pal ◽  
K Kalita
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Composite Laminates ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Static And Dynamic Analysis ◽  
Aspect Ratios ◽  
Skew Angles

This study investigates and reviews prior research works on skew composite laminates. The equivalent single layer theories are explored and discussed. An exhaustive review on static and dynamic analysis of composite skew laminates is also presented. Subsequently, a nine node isoparametric plate bending element is used for free vibration analysis of laminated composite skew plate with central skew cut out. The effect of shear deformation is incorporated in the formulation considering first order shear deformation theory. Two types of mass lumping schemes are analysed to study the effect of rotary inertia. Certain numerical examples of plates having different skew angles, skew cut out sizes, boundary conditions, thickness ratios (h/a), aspect ratios (a/b), fiber orientations and number of layers are solved which will be useful for benchmarking of future studies.

Four-Node Quadrilateral Shell Element MITC4

2016 ◽  
Vol 825 ◽  
pp. 99-104 ◽  
Author(s):  
Edita Dvořáková ◽  
Bořek Patzák
Keyword(s):  
Three Dimensional ◽  
Shell Element ◽  
Thin Shells ◽  
Element Formulation ◽  
Finite Element Code ◽  
Shear Locking ◽  
Benchmark Problem ◽  
Quadrilateral Element ◽  
Shell Elements ◽  
Continuum Description

Four-node quadrilateral element MITC4 applicable to both thick and thin shells is presented. The element formulation starts from three-dimensional continuum description degenerated to shell behavior. Shear locking, which is common problem in analysis of thin shells, is overcome by the use of MITC (Mixed Interpolation of Tensorial Components) approach. Element has been implemented into finite element code OOFEM and its performance is demonstrated on Scordelis-Lo shell, a benchmark problem frequently used in the evaluation of shell elements.

Analytical Piezoelasticity Solution for Natural Frequencies of Levy-Type Piezolaminated Plates

2019 ◽  
Vol 11 (03) ◽  
pp. 1950023 ◽  
Author(s):  
Susanta Behera ◽  
Poonam Kumari
Keyword(s):  
Natural Frequencies ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Single Layer ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Aspect Ratios ◽  
Support Conditions

First time, an analytical solution based on three-dimensional (3D) piezoelasticity is developed for the free vibration analysis of Levy-type piezolaminated plates using 3D extended Kantorovich method (EKM). Extended Hamilton principle (which is extended from elastic to piezoelectric case) is further extended to the dynamic version of mixed form containing contributions from the electrical terms. Multi-term multi-field extended Kantorovich method in conjunction with Fourier series (along [Formula: see text]-direction) is employed to obtain two sets of first-order homogeneous ordinary differential equations (8[Formula: see text] along [Formula: see text]- and [Formula: see text]-axes). A robust algorithm is designed (Fortran Code) to extract the natural frequencies and mode shapes of Levy-type piezolaminated plates. The accuracy and efficacy of this technique are verified thoroughly by comparing it with the existing results in the literature and with the 3D finite element (FE) solutions. Numerical results are presented for single-layer piezoelectric and smart sandwich plates considering five different boundary support conditions, three aspect ratios (length to thickness ratio) and electric open and close circuit conditions. The present results shall be used as a benchmark to assess various two-dimensional (2D) and 3D numerical solutions (e.g., FEM, DQM, etc.).

Sign in / Sign up

Export Citation Format

Share Document