Behavior of Unidirectional Sandwich Panels With a Bi-Linear “Soft” Core: High Order Approach

2000 ◽  
Author(s):  
Hilla Schwarts-Givli ◽  
Yeoshua Frostig
Keyword(s):  
Constitutive Relation ◽  
Constitutive Relations ◽  
Order Theory ◽  
Solution Procedure ◽  
Load Level ◽  
High Order ◽  
Core Material ◽  
Normal Stresses ◽  
Convergence Criteria ◽  
Level Increase

Abstract A closed-form high-order theory for the analysis of a sandwich panel with a core made of a material characterized by a bi-linear constitutive relation is presented. The non-linearities in the core are a result of bi-linear constitutive relations of the shear and vertical normal stresses. The governing equations are non-linear in the longitudinal and in the vertical coordinates in general. The solution procedure adopted is an iterative one along with convergence criteria. The numerical examples include two types of core material behaviors; where the first one deals with a bi-linear constitutive relation for the shear stress only; and the second one with a bi-linear constitutive relation for vertical normal stresses only. The results demonstrate the relaxation of the stress concentration involves as the load level increase beyond the yielding level as the secant modulus decrease. In the sequel, a summary and conclusions are presented.

scholarly journals Nonlocal theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

2017 ◽  
Vol 4 (1) ◽  
pp. 221-236 ◽  
Author(s):  
V.V. Zozulya
Keyword(s):  
Fourier Series ◽  
Legendre Polynomials ◽  
Fourier Coefficients ◽  
Constitutive Relations ◽  
Nonlocal Theory ◽  
Order Theory ◽  
Theory Of Elasticity ◽  
High Order ◽  
Middle Line ◽  
Curved Rods

Abstract New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

Delamination analysis of sandwich beam - High-order theory

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 981-986
Author(s):  
F. Minghui ◽  
L. Zuoqiu ◽  
Y. Jiuren
Keyword(s):  
Sandwich Beam ◽  
Order Theory ◽  
High Order ◽  
High Order Theory

New Higher-Order Models for Sandwich Plates with a Flexible Core and their Accuracy Assessment

2019 ◽  
Vol 19 (03) ◽  
pp. 1950024 ◽  
Author(s):  
Ali Tian ◽  
Renchuan Ye ◽  
Peng Ren ◽  
Pengming Jiang ◽  
Zengtao Chen ◽  
...  
Keyword(s):  
Dynamic Models ◽  
Accuracy Assessment ◽  
Order Theory ◽  
Higher Order ◽  
Analytical Models ◽  
Core Material ◽  
Sandwich Plates ◽  
Higher Order Theory ◽  
Flexible Core

Two higher-order analytical models based on a new higher-order theory for sandwich plates with flexible cores are developed considering the effect of the core material density and skin-to-core-stiffness-ratio (SCSR). The main difference between the two models is the role of the flexible core in the dynamic response of sandwich plates with cores of different stiffnesses. Firstly, the governing equations of a simply supported sandwich plate with a flexible core are derived based on the two models, and the analytical solutions are determined by using Navier’s approach. Then, the free vibration, static, dynamic bending and stress field characteristics of the sandwich plates with different SCSRs are investigated. The results obtained by the proposed method are compared with other published results. In particular, an accuracy assessment of the present dynamic models is conducted for different SCSRs. Finally, conclusions on the applicability of the proposed method and other theories on sandwich plates with different SCSRs are drawn.

A High-Order Theory of Plate Deformation—Part 2: Laminated Plates

1977 ◽  
Vol 44 (4) ◽  
pp. 669-676 ◽  
Author(s):  
K. H. Lo ◽  
R. M. Christensen ◽  
E. M. Wu
Keyword(s):  
Classical Theory ◽  
Present Theory ◽  
Order Theory ◽  
Laminated Plates ◽  
High Order ◽  
Plate Deformation ◽  
High Order Theory ◽  
Elasticity Solutions

The high-order theory of plate deformation developed in Part 1 of this work is extended here to model the behavior of laminated plates. Through comparison with elasticity solutions, it is shown the present theory correctly models effects not attainable from the classical theory.

Constitutive Relations and Parameter Estimation for Finite Deformations of Viscoelastic Adhesives

2015 ◽  
Vol 82 (2) ◽  
Author(s):  
G. O. Antoine ◽  
R. C. Batra
Keyword(s):  
Constitutive Relation ◽  
Axial Strain ◽  
Constitutive Relations ◽  
Finite Deformations ◽  
Low Velocity Impact ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Cauchy Stress ◽  
Peak Strain ◽  
Material Parameters

We propose a constitutive relation for finite deformations of nearly incompressible isotropic viscoelastic rubbery adhesives assuming that the Cauchy stress tensor can be written as the sum of elastic and viscoelastic parts. The former is derived from a stored energy function and the latter from a hereditary type integral. Using Ogden’s expression for the strain energy density and the Prony series for the viscoelastic shear modulus, values of material parameters are estimated by using experimental data for uniaxial tensile and compressive cyclic deformations at different constant engineering axial strain rates. It is found that values of material parameters using the loading part of the first cycle, the complete first cycle, and the complete two loading cycles are quite different. Furthermore, the constitutive relation with values of material parameters determined from the monotonic loading during the first cycle of deformations cannot well predict even deformations during the unloading portion of the first cycle. The developed constitutive relation is used to study low-velocity impact of polymethylmethacrylate (PMMA)/adhesive/polycarbonate (PC) laminate. The three sets of values of material parameters for the adhesive seem to have a negligible effect on the overall deformations of the laminate. It is attributed to the fact that peak strain rates in the severely deforming regions are large, and the corresponding stresses are essentially unaffected by the long time response of the adhesive.

Delamination Analysis of Sandwich Beam: High-Order Theory

AIAA Journal ◽  
2002 ◽  
Vol 40 (5) ◽  
pp. 981-986 ◽  
Author(s):  
Fu Minghui ◽  
Liu Zuoqiu ◽  
Yin Jiuren
Keyword(s):  
Sandwich Beam ◽  
Order Theory ◽  
High Order ◽  
High Order Theory

Parameter Estimation of the Mechanical Behavior of the Artery Using a Nonlinear Least Square Method With a Noise Model

2008 ◽  
Author(s):  
Shahrokh Zeinali ◽  
Jongeun Choi ◽  
Seungik Baek
Keyword(s):  
Parameter Estimation ◽  
Blood Vessel ◽  
Mechanical Behavior ◽  
Constitutive Relation ◽  
Environmental Changes ◽  
Constitutive Relations ◽  
Estimation Method ◽  
Least Square ◽  
Noise Model ◽  
Bias Error

Although it is well known that blood vessels adapt and remodel in response to various biomechanical stimuli, quantifying changes in constitutive relation corresponding to environmental changes is still challenging. Especially, when the dimension of blood vessel is small, the uncertainties in experimental measurements become significant and make it difficult to precisely estimate parameters of constitutive relations for mechanical behavior of the blood vessel. Hence without considering measurement error in displacement, a conventional nonlinear least square (NLS) method results in a biased parameter estimation. In this paper, we propose a new parameter estimation method to eliminate such bias error and provide more accurate estimated parameters for a constitutive relation using a weighted nonlinear least square (WNLS) method with a noise model. We first applied the proposed technique to a set of synthesized data with computer generated white noises and compared the fitting results to those of the NLS method without the noise model. We also applied our method to experimental data sets from mechanical tests of rabbit basilar and mouse carotid arteries and studied parameter sensitivity of the constitutive model.

Simulation of Frictional Sliding Under Impact Shear Loading

2004 ◽  
Author(s):  
Demir Coker ◽  
Alan Needleman ◽  
George Lykotrafitis ◽  
Ares J. Rosakis
Keyword(s):  
Constitutive Relation ◽  
Wave Speed ◽  
Constitutive Relations ◽  
Shear Loading ◽  
Stress And Strain ◽  
Sliding Modes ◽  
Elastic Plates ◽  
Frictional Sliding ◽  
State Dependent ◽  
Dynamic Loading Conditions

Results from recent and ongoing investigations of frictional sliding under dynamic loading conditions are discussed. The configuration analyzed consists of two identical elastic plates with an interface characterized by a rate- and state-dependent frictional law. The calculations are carried out within a framework where two constitutive relations are used: a volumetric constitutive relation between stress and strain and a surface constitutive relation that characterizes the frictional behavior of the interface. The simulations discussed predict a variety of sliding modes including a crack-like mode and several pulse-like modes as well as circumstances where the sliding tip speed can exceed the longitudinal wave speed.

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