A Constraint on the Consistence of Transverse Shear Strain Energy in the Higher-Order Shear Deformation Theories of Elastic Plates

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
Guangyu Shi ◽  
Xiaodan Wang
Keyword(s):  
Shear Strain ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Strain Energy ◽  
Higher Order ◽  
Transverse Shear Strain ◽  
Displacement Fields ◽  
Shear Deformations ◽  
Third Order ◽  
Shear Strain Energy

This paper studies how to improve the third-order shear deformation theories of isotropic plates, which is a question raised by late Reissner in 1985 (ASME Appl. Mech. Rev., 38, pp.1453–1464). It is demonstrated in this paper that a proper displacement field with the higher-order shear deformations given by the method of displacement assumption should satisfy the constraint on the consistence of the transverse shear strain energy a priori in addition to the traction conditions on plate surfaces. This additional constraint on the assumed displacement fields with the higher-order shear deformations is in line with Love's criterion of the consistent first approximation to the strain energy wherein the transverse shear strain energy is included. The constraint on the consistence of the transverse shear strain energy is physically similar to the requirement for the use of the shear coefficients in the first-order shear deformation plate theories proposed by Reissner and Mindlin, respectively. A procedure to improve the assumed displacement field with the third-order shear deformations is presented. The present study shows that the various displacement fields with the simple third-order shear deformations would be identical when the constraint on the consistence of the transverse shear strain energy is enforced.

A Higher-Order Theory for Vibration Analysis of Curvilinear Thick Shallow Shells with Constrained Boundaries

1995 ◽  
Vol 1 (1) ◽  
pp. 15-39 ◽  
Author(s):  
K.M. Liew ◽  
C.W. Lim
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Vibration Analysis ◽  
Numerical Procedure ◽  
Higher Order ◽  
Mode Shapes ◽  
Transverse Shear Strain ◽  
Shallow Shells ◽  
Displacement Mode ◽  
Wide Range

This article presents the vibration analysis of thick doubly curved shallow shells having curvilinear planform. The Gaussian curvature of shell varies from positive (such as spherical) to negative (such as hyperbolic paraboloidal). The boundaries are constrained with either soft-simply supported or fully clamped edges. A higher-order shear deformation theory, which includes transverse shear strain and rotary inertia, is developed to model the vibration characteristics of the shell. The inclusion of Lamé parameters in the present formulation accounts for the presence of shell curvature and yields cubic transverse shear strain distribution in contrast with the existing quadratic expressions. A set of versatile, globally continuous shape functions is adopted in the Ritz numerical procedure to approximate the displacement and rotation fields. A set of new results for a wide range of shell configurations is presented with some selected contour and three-dimensional displacement mode shapes.

On the nominal transverse shear strain to characterize the severity of creasing

TAPPI Journal ◽  
2018 ◽  
Vol 17 (04) ◽  
pp. 231-240
Author(s):  
Douglas Coffin ◽  
Joel Panek
Keyword(s):  
Shear Strain ◽  
Transverse Shear ◽  
Elastic Limit ◽  
Experimental Results ◽  
Transverse Shear Strain ◽  
Maximum Strain ◽  
Machine Direction ◽  
Engineering Approach ◽  
Wide Range ◽  
Analytic Expression

A transverse shear strain was utilized to characterize the severity of creasing for a wide range of tooling configurations. An analytic expression of transverse shear strain, which accounts for tooling geometry, correlated well with relative crease strength and springback as determined from 90° fold tests. The experimental results show a minimum strain (elastic limit) that needs to be exceeded for the relative crease strength to be reduced. The theory predicts a maximum achievable transverse shear strain, which is further limited if the tooling clearance is negative. The elastic limit and maximum strain thus describe the range of interest for effective creasing. In this range, cross direction (CD)-creased samples were more sensitive to creasing than machine direction (MD)-creased samples, but the differences were reduced as the shear strain approached the maximum. The presented development provides the foundation for a quantitative engineering approach to creasing and folding operations.

The Creep of Thick Tubes Under Internal Pressure

1957 ◽  
Vol 24 (3) ◽  
pp. 464-466
Author(s):  
C. D. Weir
Keyword(s):  
Internal Pressure ◽  
Strain Rate ◽  
Shear Strain ◽  
Rate Equation ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Stress Deviator ◽  
Constant Density ◽  
Creep Stress ◽  
Shear Strain Energy

Abstract Using the usually accepted assumption that the strain rate of a material undergoing creep is given by the product of the stress deviator and a function of the shear-strain energy, and assuming constant density, equations are derived for the creep stresses in a thick-walled tube under internal pressure for a generalized form of the shear strain-energy function. It is shown that these reduce to previously published equations on the substitution of a power law stress-strain rate equation. The nonisothermal case is considered also and creep-stress equations are obtained in a similarly generalized form.

scholarly journals Investigation of porosity effect on flexural analysis of doubly curved FGM conoids

2019 ◽  
Vol 26 (1) ◽  
pp. 435-448
Author(s):  
Md Irfan Ansari ◽  
Ajay Kumar ◽  
Danuta Barnat-Hunek ◽  
Zbigniew Suchorab ◽  
Bartłomiej Kwiatkowski
Keyword(s):  
Mathematical Model ◽  
Shear Strain ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Current Model ◽  
Lower Surface ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Flexural Analysis ◽  
Doubly Curved

AbstractThe flexural analysis of doubly curved functionally graded porous conoids was performed in the present paper. The porosities inside functionally graded materials (FGMs) can occur during the fabrication and lead to the occurrence of micro-voids in the materials. The mathematical model includes expansion of Taylor’s series up to the third degree in thickness coordinate and normal curvatures in in-plane displacement fields. Since there is a parabolic variation in transverse shear strain deformation across the thickness coordinate, the shear correction factor is not necessary. The condition of zero-transverse shear strain at upper and lower surface of conoidal shell is implemented in the present model. The improvement in the 2D mathematical model enables to solve problems of moderately thick FGM porous conoids. The distinguishing feature of the present shell from the other shells is that maximum transverse deflection does not occur at its centre. The improved mathematical model was implemented in finite element code written in FORTRAN. The obtained numerical results were compared with the results available in the literature. Once validated, the current model was employed to study the effect of porosity, boundary condition, volume fraction index, loading pattern and others geometric parameters.

Stress analysis of smart composite plate structures

2020 ◽  
pp. 095440622097544
Author(s):  
Aniket Chanda ◽  
Utkarsh Chandel ◽  
Rosalin Sahoo ◽  
Neeraj Grover
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Laminated Composite ◽  
Composite Plates ◽  
Higher Order ◽  
Hyperbolic Function ◽  
Solution Technique ◽  
Shear Stresses ◽  
Laminated Composite Plates ◽  
Equilibrium Equations

In the present study, the electro-mechanical responses of smart laminated composite plates with piezoelectric materials are derived using a two-dimensional (2 D) displacement-based non-polynomial higher-order shear deformation theory. The kinematics of the mathematical model incorporates the deformation of laminates which account for the effects of transverse shear deformation and a non-linear variation of the in-plane displacements using inverse sine hyperbolic function of the thickness coordinate. The equilibrium equations are obtained using the minimization of energy principle known as the principle of minimum potential energy (PMPE) which is also based on a variational approach and the solutions are obtained using Navier’s solution technique for diaphragm supported smart laminated composite plates. The responses obtained in the form of deflection and stresses are compared with three dimensional (3 D) solutions and also with different polynomial and non-polynomial based higher-order theories in the literature. The transverse shear stresses are obtained using 3 D equilibrium equations of elasticity to enhance the accuracy of the present results. Various examples are numerically solved to establish the efficiency of the present model.

Minimum-weight beams with shear strain energy

2011 ◽  
Vol 16 (1) ◽  
pp. 145-154 ◽  
Author(s):  
Byoung Koo Lee ◽  
Sang Jin Oh ◽  
Tae Eun Lee ◽  
Jung Su Park
Keyword(s):  
Shear Strain ◽  
Strain Energy ◽  
Minimum Weight ◽  
Shear Strain Energy
Sign in / Sign up

Export Citation Format

Share Document