2D Elastodynamic Solution for the Impact Response of Laminated Composites

2013 ◽  
Vol 81 (4) ◽  
Author(s):  
Jiawen Xie ◽  
Anthony M. Waas
Keyword(s):  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Transverse Impact ◽  
Multilayered Structures ◽  
Arbitrary Loading ◽  
Expansion Technique ◽  
Transverse Stresses ◽  
Elastodynamic Solution ◽  
The Impact

This paper presents a general, exact, two-dimensional (2D) elastodynamic analysis of the response of laminated composite panels subjected to transverse impact loading under conditions of planar deformation. The natural frequencies and mode shapes of free vibration are first extracted. Inspired by a transformation technique for solving a special class of partial differential equations, the forced vibration problem of an impacted laminated panel is solved using an eigenfunction expansion technique. Several examples are studied by varying the laminate lay-up and length-to-thickness ratio. The distributions of transverse stresses in the through-the-thickness direction are further compared with two one-dimensional theories, classical lamination theory (CLT) and first-order shear deformation theory (FSDT), showing the inadequacy of these theories and the necessity to establish a benchmark solution for 2D elastodynamics. The 2D elastodynamic theory that is formulated is also applicable for studying other multilayered structures subjected to arbitrary loading profiles.

scholarly journals Fundamental Frequency of Laminated Composite Thick Spherical Shells

2019 ◽  
Vol 11 (1) ◽  
pp. 57
Author(s):  
Mohammad Zannon
Keyword(s):  
Shear Deformation ◽  
Equations Of Motion ◽  
Minimum Energy ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Composite Shells ◽  
Software Packages ◽  
Element Technique ◽  
Laminated Composite Shells

In this study, we apply third-order shear deformation thick shell theory to analytically derive the frequency characteristics of the free vibration of thick spherical laminated composite shells. The equations of motion are derived using Hamilton’s principle of minimum energy and on the basis of the relationships between forces, moments, and stress displacements in the shell. We confirm the derived equations and analytical results through the finite element technique by using the well-known software packages MATLAB and ANSYS. We consider the fundamental natural frequencies and the mode shapes of simply supported spherical cross-ply (0, 90), (0, 90, 0), and (0, 90, 90, 0) laminated composite shells. Then, to increase accuracy and decrease calculation efforts, we compare the results obtained through classical theory and first-order shear deformation theory.

Influence of openings and additional mass on vibration of laminated sandwich rhombic plates using IHSDT

2018 ◽  
Vol 33 (1) ◽  
pp. 3-34 ◽  
Author(s):  
Anish ◽  
Ajay Kumar ◽  
Anupam Chakrabarti
Keyword(s):  
Shear Stress ◽  
Free Vibration ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Fe Model ◽  
Additional Mass ◽  
Interlaminar Shear ◽  
Piecewise Parabolic

In this article, investigations on the influence of openings and additional mass on free vibration analysis of laminated composite sandwich skew plates using improved higher order shear deformation theory (IHSDT) have been done. The IHSDT model satisfies the interlaminar shear stress continuity at the layer interfaces and also ensures zero transverse shear stress conditions at the top and bottom of the plate. The piecewise parabolic shear stress variation across the thickness of each layer is considered. No shear correction factors are required. The 2-D C0 finite element (FE) model has been developed by authors based on IHSDT. FE model based on IHSDT has been coded in FORTRAN. The problem of C1 continuity requirement associated with the IHSDT is overcome using an appropriate C0 FE formulation. The free vibration frequencies of laminated composite and sandwich plates obtained using the present 2-D FE model are in good agreement with the 3-D elasticity results. The influence of the side-to-thickness ratio, skew angles, boundary conditions, and mode shapes is taken into consideration for the present study.

STATIC AND DYNAMIC BEHAVIOUR OF LAMINATED COMPOSITE BEAMS

2001 ◽  
Vol 01 (04) ◽  
pp. 545-560 ◽  
Author(s):  
M. A. RAMOS LOJA ◽  
J. INFANTE BARBOSA ◽  
C. M. MOTA SOARES
Keyword(s):  
Cross Sections ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Laminated Composite ◽  
Element Model ◽  
Composite Beams ◽  
Straight Beam ◽  
Transverse Stresses

A higher order shear deformation theory, assuming a non-linear variation for the displacement field, is used to develop a finite element model to predict static and free vibration behaviour of anisotropic multilaminated thick and thin beams. The model is based on a single-layer Lagrangean four-node straight beam element with fourteen degrees of freedom per node. It considers bending into two orthogonal planes, stretching and twisting to enable three-dimensional analysis of frames. The most common cross sections and symmetric and asymmetric lay-ups are studied. The behaviour of the model is tested on thin and thick isotropic and composite beams. Comparisons show that the model is accurate and versatile. The good performance of the present model is evident on the prediction of displacements, normal and transverse stresses and natural frequencies of thin and thick isotropic or anisotropic beam structures.

Natural Frequencies and Mode Shapes of Laminated Composite Skew Hypar Shells with Complicated Boundary Conditions Using Finite Element Method

2012 ◽  
Vol 585 ◽  
pp. 44-48 ◽  
Author(s):  
Ajay Kumar ◽  
Pradeep Bhargava ◽  
Anupam Chakrabarti
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Higher Order ◽  
Finite Element Formulation ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Element Formulation

In the present investigation, free vibration behaviour is studied for the laminated composite skew hypar shells having twist radius of curvature. A higher-order shear deformation theory is employed in the C0 finite element formulation. Higher-order terms in the Taylor’s series expansion are used to represent the higher-order transverse cross sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effect of transverse shear. The structural system is considered to be undamped. The correctness of the formulation is established by comparing the present results of problems with those available in the published literature. The effects of different parameters are studied on the free vibration aspects of laminated composite skew hypar shells. Effect of cross curvature is included in the formulation. The C0 finite element formulation has been done quite efficiently to overcome the problem of C1 continuity associated with the HSDT. The isoparametric FE used in the present model consists of nine nodes with seven nodal unknowns per node. Since there is no result available in the literature based on HSDT on the problem of free vibration of laminated composite skew hypar shells, new results are presented by varying geometry, boundary conditions, ply orientations and skew angles which will serve as benchmark for future researchers.

Large Amplitude Vibrations of Laminated Rectangular Plates With Free Edges

2013 ◽  
Author(s):  
F. Alijani ◽  
M. Amabili
Keyword(s):  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Energy Functional ◽  
Harmonic Excitation ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Collocation Scheme ◽  
Large Amplitude Vibrations

Nonlinear forced vibrations of completely free laminated composite rectangular plates are studied using multi-modal Lagrangian approach. Nonlinear higher-order shear deformation theory is used and the nonlinear response to transverse harmonic excitation in the frequency neighborhood of the fundamental mode is investigated. The numerical analysis is conducted in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is performed to obtain the natural frequencies and mode shapes. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with cubic and quadratic nonlinear terms is obtained. A pseudo arc-length continuation and collocation scheme is employed to carry out a bifurcation analysis. A consistent reduced-order model necessary to capture the nonlinear dynamics of the plate is developed and the effect of number of modes retained in the numerical model is discussed.

Dynamic model for high-speed rotors based on their experimental characterization

2017 ◽  
Vol 2 (4) ◽  
pp. 25
Author(s):  
L. A. Montoya ◽  
E. E. Rodríguez ◽  
H. J. Zúñiga ◽  
I. Mejía
Keyword(s):  
Dynamic Model ◽  
High Speed ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Experimental Characterization ◽  
Rotating Systems ◽  
Computing Performance ◽  
The Impact ◽  
Stiffness Distribution ◽  
Good Agreement

Rotating systems components such as rotors, have dynamic characteristics that are of great importance to understand because they may cause failure of turbomachinery. Therefore, it is required to study a dynamic model to predict some vibration characteristics, in this case, the natural frequencies and mode shapes (both of free vibration) of a centrifugal compressor shaft. The peculiarity of the dynamic model proposed is that using frequency and displacements values obtained experimentally, it is possible to calculate the mass and stiffness distribution of the shaft, and then use these values to estimate the theoretical modal parameters. The natural frequencies and mode shapes of the shaft were obtained with experimental modal analysis by using the impact test. The results predicted by the model are in good agreement with the experimental test. The model is also flexible with other geometries and has a great time and computing performance, which can be evaluated with respect to other commercial software in the future.

scholarly journals Non-linear deflection and stress analysis of laminated composite sandwich plate with elliptical cutout under different transverse loadings in hygro-thermal environment

2020 ◽  
Vol 7 (1) ◽  
pp. 80-100
Author(s):  
Rahul Kumar ◽  
Achchhe Lal ◽  
B. M. Sutaria
Keyword(s):  
Stress Concentration ◽  
Sandwich Plate ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Gauss Point ◽  
Composite Sandwich ◽  
Aspect Ratios ◽  
Present Solution ◽  
Non Linear

AbstractIn this paper, non-linear transverse deflection, stress and stress concentration factors (SCF) of isotropic and laminated composite sandwich plate (LCSP) with and without elliptical cutouts subjected to various trans-verse loadings in hygrothermal environment are studied. The basic formulation is based on secant function-based shear deformation theory (SFSDT) with von-Karman nonlinearity. The governing equation of non-linear deflection is derived using C0 finite element method (FEM) through minimum potential energy approach. Normalized trans-verse maximum deflections (NTMD) along with stress concentration factor is determined by using Newton’s Raphson method through Gauss point stress extrapolation. Influence of fiber orientations, load parameters, fiber volume fractions, plate span to thickness ratios, aspect ratios, thickness of core and face, position of core, boundary conditions, environmental conditions and types of transverse loading in MATLAB R2015a environment are examined. The numerical results using present solution methodology are verified with the results available in the literatures.

scholarly journals Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Trung Thanh Tran ◽  
Van Ke Tran ◽  
Pham Binh Le ◽  
Van Minh Phung ◽  
Van Thom Do ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Thermal Environments ◽  
Forced Vibration Analysis ◽  
Laminated Composite Shells ◽  
Element Method

This paper carries out forced vibration analysis of graphene nanoplatelet-reinforced composite laminated shells in thermal environments by employing the finite element method (FEM). Material properties including elastic modulus, specific gravity, and Poisson’s ratio are determined according to the Halpin–Tsai model. The first-order shear deformation theory (FSDT), which is based on the 8-node isoparametric element to establish the oscillation equation of shell structure, is employed in this work. We then code the computing program in the MATLAB application and examine the verification of convergence rate and reliability of the program by comparing the data of present work with those of other exact solutions. The effects of both geometric parameters and mechanical properties of materials on the forced vibration of the structure are investigated.

Natural Frequency of Laminated Composite Plates Using a Sinusoidal Theory

2014 ◽  
Vol 709 ◽  
pp. 148-152
Author(s):  
Guo Qing Zhou ◽  
Ji Wang ◽  
Song Xiang
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Sinusoidal Shear Deformation Theory

Sinusoidal shear deformation theory is presented to analyze the natural frequencies of simply supported laminated composite plates. The governing differential equations based on sinusoidal theory are solved by a Navier-type analytical method. The present results are compared with the available published results which verify the accuracy of sinusoidal theory.

Sign in / Sign up

Export Citation Format

Share Document