scholarly journals Dynamic Analysis of Sandwich Auxetic Honeycomb Plates Subjected to Moving Oscillator Load on Elastic Foundation

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Thanh Trung Tran ◽  
Quoc Hoa Pham ◽  
Trung Nguyen-Thoi ◽  
The-Van Tran
Keyword(s):  
Dynamic Response ◽  
Elastic Foundation ◽  
Plate Theory ◽  
Structural Parameters ◽  
Composite Plates ◽  
Sandwich Composite ◽  
Mindlin Plate ◽  
Response Analysis ◽  
Direct Integration Method ◽  
Moving Oscillator

Based on Mindlin plate theory and finite element method (FEM), dynamic response analysis of sandwich composite plates with auxetic honeycomb core resting on the elastic foundation (EF) under moving oscillator load is investigated in this work. Moving oscillator load includes spring-elastic k and damper c. The EF with two coefficients was modelled by Winkler and Pasternak. The system of equations of motion of the sandwich composite plate can be solved by Newmark’s direct integration method. The reliability of the present method is verified through comparison with the results other methods available in the literature. In addition, the effects of structural parameters, material properties, and moving oscillator loads to the dynamic response of the auxetic honeycomb plate are studied.

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.

Frequency Response of a Three-Node Finite Element for Composite Thin and Thick Plates

2004 ◽  
Author(s):  
A. V. S. Ravi Shastry ◽  
Pramod Kumar
Keyword(s):  
Finite Element ◽  
Frequency Response ◽  
Plate Theory ◽  
Composite Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Integration Scheme ◽  
Shear Locking ◽  
Triangular Finite Element ◽  
Strain Components

A shear-locking free isoparametric three-node triangular finite element is considered for the study of frequency response of moderately thick and thin composite plates. The strain displacement relationship is based on Reissner-Mindlin plate theory that accounts for transverse shear deformations into the plate formulation to circumvent the shear locking effect. The element is developed with full integration scheme; hence the element remains kinematically stable. The performance of the element for the case of static load response using the shear correction terms to shear strain components applied to a composite plate has been studied. The natural frequencies and mode shapes in accordance with varying mode numbers, are deduced and the results are compared with the available analytical and finite element solutions in literature.

Advanced Plate Theory for Multibody Dynamics

2013 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Shilei Han
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Hamiltonian Formalism ◽  
Laminated Composite ◽  
Composite Plates ◽  
Complex Stress State ◽  
Mindlin Plate ◽  
Element Discretization ◽  
Deformation State ◽  
Material Line

In flexible multibody systems, many components are often approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theory, form the basis of the analytical development for plate dynamics. The advantage of this approach is that it leads to a very simple kinematic representation 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 a three-dimensional deformation state that generates a complex stress state. To overcome this problem, several high-order and refined plate theory were proposed. While these approaches work well for some cases, they typically lead to inefficient formulation because they introduce numerous additional variables. This paper presents a different approach to the problem, which is based on a finite element discretization of the normal material line, and relies of the Hamiltonian formalism of obtain solutions of the governing equations. Polynomial solutions, also known as central solutions, are obtained that propagate over the entire span of the plate.

Overestimation Analysis of Interval Finite Element for Structural Dynamic Response

2019 ◽  
Vol 11 (04) ◽  
pp. 1950035
Author(s):  
Tuanjie Li ◽  
Hangjia Dong ◽  
Xi Zhao ◽  
Yaqiong Tang
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Structural Parameters ◽  
Upper And Lower Bounds ◽  
Response Analysis ◽  
Uncertain Parameters ◽  
Engineering Structures ◽  
Structural Dynamic ◽  
Dynamic Response Analysis ◽  
Interval Parameters

Dynamic response analysis plays an important role for the structural design. For engineering structures, there exist model inaccuracies and structural parameters uncertainties. Consequently, it is necessary to express these uncertain parameters as interval variables and introduce the interval finite element method (IFEM), in which the elements in stiffness matrix, mass matrix and damping matrix are all the function of interval parameters. The dependence of interval parameters leads to overestimation of dynamic response analysis. In order to reduce the overestimation of IFEM, the element-based subinterval perturbation for static analysis is applied to dynamic response analysis. According to the interval range, the interval parameters are divided into different subintervals. With permutation and combination of each subinterval, the upper and lower bounds of displacement response are obtained. Because of the large number of degrees of freedom and uncertain parameters, the Laplace transform is used to evaluate the dynamic response for avoiding to frequently solve the interval finite element linear equations. The numerical examples illustrate the validity and feasibility of the proposed method.

scholarly journals Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

2020 ◽  
Vol 41 (12) ◽  
pp. 1769-1786
Author(s):  
Wenjie Feng ◽  
Zhen Yan ◽  
Ji Lin ◽  
C. Z. Zhang
Keyword(s):  
Elastic Foundation ◽  
Plate Theory ◽  
Nonlocal Theory ◽  
Mindlin Plate ◽  
Governing Equations ◽  
General Applicability ◽  
Particular Solutions ◽  
Pasternak Elastic Foundation ◽  
Mindlin Plate Theory ◽  
Selection Of

AbstractBased on the nonlocal theory and Mindlin plate theory, the governing equations (i.e., a system of partial differential equations (PDEs) for bending problem) of magnetoelectroelastic (MEE) nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle. The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions (MPS) to solve the governing equations numerically. It is confirmed that for the present bending model, the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points. Finally, the effects of different boundary conditions, applied loads, and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method. Some important conclusions are drawn, which should be helpful for the design and applications of electromagnetic nanoplate structures.

Comparison of Free Flexural Vibrations of Composite Plates or Panels Stiffened by a Central and a Non-Central Plate Strip

1999 ◽  
Author(s):  
U. Yuceoglu ◽  
V. Özerciyes
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Composite Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Solution Technique ◽  
Orthotropic Plates ◽  
Bending Vibration ◽  
Central Plate ◽  
Plate Strip

Abstract The natural frequencies and the corresponding mode shapes of two classes of composite base plate or panel stiffened by a central or a non-central plate strip are analyzed and compared with each other. In each case, the base plates and the single, stiffening plate strips are assumed to be dissimilar orthotropic plates connected by a very thin, yet deformable adhesive layer. The free bending vibration problems for the two cases are formulated in terms of the Mindlin Plate Theory for orthotropic plates. The governing equations are reduced to a system of first order equations. The solution technique is the “Modified Version of the Transfer Matrix Method”. The effects of the bonded central and non-central stiffening strip on the mode shapes and the natural frequencies of the composite plate or panel system are investigated. Some important conclusions are drawn from the numerical and parametric studies presented.

Enhanced Elastic Buckling Loads of Composite Plates With Tailored Thermal Residual Stresses

1997 ◽  
Vol 64 (4) ◽  
pp. 772-780 ◽  
Author(s):  
S. F. Mu¨ller de Almeida ◽  
J. S. Hansen
Keyword(s):  
Residual Stresses ◽  
Plate Theory ◽  
Design Procedure ◽  
Composite Plates ◽  
Buckling Load ◽  
Mindlin Plate ◽  
Buckling Loads ◽  
Thermal Residual Stresses ◽  
Element Technique ◽  
Lagrange Element

Thermal residual stresses introduced during the manufacturing process and their effect on the buckling load of stringer reinforced composite plates is investigated. The principal idea is to include stiffeners on the perimeter of the plate and thereby, during manufacture, induce a favorable thermal residual-stress state in the structure; these stresses arise by considering the difference in thermal expansion coefficients and elastic properties of the plate and the stiffeners. In this manner, it is shown that thermal residual stresses can be tailored to significantly enhance the performance of the structure. The analysis is taken within the context of an enhanced Reissner-Mindlin plate theory and the finite element technique is used to analyze the problem. A 16 node bi-cubic Lagrange element is implemented in a FORTRAN code to determine the buckling load of the composite plate in the presence of thermal residual stresses. Three different plate-stiffener geometries are used as illustrations. The analyses indicate that buckling loads can be significantly increased by properly tailoring the thermal residual stresses. Therefore it may be concluded that an evaluation of these stresses and a judicious analysis of their effects must be included in the design procedure for this class of composite structure.

scholarly journals An Analytical Method for Evaluating the Dynamic Response of Plates Subjected to Underwater Shock Employing Mindlin Plate Theory and Laplace Transforms

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zhenyu Wang ◽  
Xu Liang ◽  
Guohua Liu
Keyword(s):  
Dynamic Response ◽  
Response Time ◽  
Analytical Method ◽  
Extreme Values ◽  
Plate Theory ◽  
Underwater Explosion ◽  
Mindlin Plate ◽  
Time Histories ◽  
Mindlin Plate Theory ◽  
Benchmark Solutions

It is often in the interest of a designer to know the transient state of stress in a plate subjected to an underwater explosion. In this paper, an analytical method based on Taylor’s fluid-solid interaction (FSI) model, Mindlin plate theory, Laplace transform, and its inversion is proposed to examine the elastic dynamic response of a plate subjected to an underwater explosion. This analytical method includes shear deformation, the moments and membrane stress in the plate, and the FSI effect and considers a full profile of possibilities. The results of the response-time histories and the response distribution on the plate in terms of displacements and stresses from the analytical method are compared with finite element analysis (FEA) to validate this method, and the comparison indicates good agreement. Comparison of the acceleration at the center of an air-backed plate between the analytical method and the experiment from relevant literature, shows good agreements, and the analytical method and its FSI model are validated. The influence of the FSI is investigated in detail. All extreme values of the response-time histories decrease as the thickness increases for the non-FSI case. The results can be used as benchmark solutions in further research.

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