Coupled higher order and mixed layerwise finite element based static and free vibration analyses of laminated plates

2015 ◽  
Vol 128 ◽  
pp. 406-414 ◽  
Author(s):  
U.N. Band ◽  
Y.M. Desai
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Higher Order ◽  
Laminated Plates

An hp-version adaptive finite element algorithm for eigensolutions of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yongliang Wang ◽  
Jianhui Wang
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Higher Order ◽  
Wave Number ◽  
Adaptive Finite Element ◽  
Content Type ◽  
Circular Cylindrical Shells ◽  
Geometrical Factors ◽  
Circumferential Wave

PurposeThis study presents a novel hp-version adaptive finite element method (FEM) to investigate the high-precision eigensolutions of the free vibration of moderately thick circular cylindrical shells, involving the issues of variable geometrical factors, such as the thickness, circumferential wave number, radius and length.Design/methodology/approachAn hp-version adaptive finite element (FE) algorithm is proposed for determining the eigensolutions of the free vibration of moderately thick circular cylindrical shells via error homogenisation and higher-order interpolation. This algorithm first develops the established h-version mesh refinement method for detecting the non-uniform distributed optimised meshes, where the error estimation and element subdivision approaches based on the superconvergent patch recovery displacement method are introduced to obtain high-precision solutions. The errors in the vibration mode solutions in the global space domain are homogenised and approximately the same. Subsequently, on the refined meshes, the algorithm uses higher-order shape functions for the interpolation of trial displacement functions to reduce the errors quickly, until the solution meets a pre-specified error tolerance condition. In this algorithm, the non-uniform mesh generation and higher-order interpolation of shape functions are suitable for addressing the problem of complex frequencies and modes caused by variable structural geometries.FindingsNumerical results are presented for moderately thick circular cylindrical shells with different geometrical factors (circumferential wave number, thickness-to-radius ratio, thickness-to-length ratio) to demonstrate the effectiveness, accuracy and reliability of the proposed method. The hp-version refinement uses fewer optimised meshes than h-version mesh refinement, and only one-step interpolation of the higher-order shape function yields the eigensolutions satisfying the accuracy requirement.Originality/valueThe proposed combination of methodologies provides a complete hp-version adaptive FEM for analysing the free vibration of moderately thick circular cylindrical shells. This algorithm can be extended to general eigenproblems and geometric forms of structures to solve for the frequency and mode quickly and efficiently.

A Comparison of Closed-Form and Finite-Element Solutions for the Free Vibration of Hybrid Cross-Ply Laminated Plates

2019 ◽  
Vol 55 (2) ◽  
pp. 181-194 ◽  
Author(s):  
M. A. Benhenni ◽  
B. Adim ◽  
T. Hassaine Daouadji ◽  
B. Abbès ◽  
F. Abbès ◽  
...  
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Closed Form ◽  
Laminated Plates ◽  
Hybrid Cross

Free Vibration Response of Thin and Thick Nonhomogeneous Shells by Refined One-Dimensional Analysis

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Alberto Varello ◽  
Erasmo Carrera
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Cross Section ◽  
Vibration Analysis ◽  
Plane Deformation ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Variable Order ◽  
Vibrational Modes ◽  
One Dimensional

The free vibration analysis of thin- and thick-walled layered structures via a refined one-dimensional (1D) approach is addressed in this paper. Carrera unified formulation (CUF) is employed to introduce higher-order 1D models with a variable order of expansion for the displacement unknowns over the cross section. Classical Euler–Bernoulli (EBBM) and Timoshenko (TBM) beam theories are obtained as particular cases. Different kinds of vibrational modes with increasing half-wave numbers are investigated for short and relatively short cylindrical shells with different cross section geometries and laminations. Numerical results of natural frequencies and modal shapes are provided by using the finite element method (FEM), which permits various boundary conditions to be handled with ease. The analyses highlight that the refinement of the displacement field by means of higher-order terms is fundamental especially to capture vibrational modes that require warping and in-plane deformation to be detected. Classical beam models are not able to predict the realistic dynamic behavior of shells. Comparisons with three-dimensional elasticity solutions and solid finite element solutions prove that CUF provides accuracy in the free vibration analysis of even short, nonhomogeneous thin- and thick-walled shell structures, despite its 1D approach. The results clearly show that bending, radial, axial, and also shell lobe-type modes can be accurately evaluated by variable kinematic 1D CUF models with a remarkably lower computational effort compared to solid FE models.

scholarly journals A new finite element for free vibration analysis of stiffened composite plates

2007 ◽  
Vol 29 (4) ◽  
pp. 529-538 ◽  
Author(s):  
Tran Ich Thinh ◽  
Ngo Nhu Khoa
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Laminated Plates ◽  
Triangular Element ◽  
Plate Element ◽  
Stiffened Plate

A new 6-noded stiffened triangular plate element for the analysis of stiffened composite plates based on Mindlins deformation plate theory has been developed. The stiffened plate element is a combination of basic triangular element and bar component. The element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffeners. Free vibration analyses of stiffened laminated plates have been carried out with this element and the results are compared with those published. The finite element results show very good matching with the experimental ones.

scholarly journals Buckling and postbuckling behavior of shell type structures under thermo-mechanical loads

2021 ◽  
pp. 79-79
Author(s):  
Zoran Vasic ◽  
Katarina Maksimovic ◽  
Mirko Maksimovic ◽  
Ivana Vasovic ◽  
Nenad Vidanovic ◽  
...  
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Composite Laminates ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Thermal Buckling ◽  
Laminated Plates ◽  
Postbuckling Behavior ◽  
Mechanical Loads ◽  
Shell Type

The thermomechanical buckling and postbuckling behavior of layered composite shell type structure are considered with the finite element method (FEM) under the combination of temperature load and applied mechanical loads. To account for through-thickness shear deformation effects, the thermal elastic, Higher-Order Shear deformation Theory (HOST) is used in this study. The refined higher order theories, that takes into account the effect of transverse normal deformation, is used to develop discrete finite element models for the thermal buckling analysis of composite laminates. Attention in this study is focused on analyzing the temperature effects on buckling and postbuckling behavior of thin shell structural components. Special attention in this paper is focused on studying of values of the hole in curved panel on thermal buckling behavior and consequently to expend and upgrade previously conducted investigation. Using FEM, a broader observation of the critical temperature of loss of stability depending on the size of the hole was conducted. The presented numerical results based on HOST can be used as versatile and accurate method for buckling and postbuckling analyzes of thin-walled laminated plates under thermo-mechanical loads.

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