scholarly journals CRITICAL LATERAL LOAD ANALYSIS OF RECTANGULAR PLATE CONSIDERING SHEAR DEFORMATION EFFECT

2020 ◽  
pp. 16-27
Author(s):  
F. C. Onyeka
Keyword(s):  
Potential Energy ◽  
Shear Deformation ◽  
Rectangular Plate ◽  
Thick Plate ◽  
Shear Deformation Theory ◽  
Lateral Load ◽  
Width Ratio ◽  
Total Potential ◽  
Transverse Loads ◽  
Total Failure

This work present flexural analysis of rectangular plate subjected to uniform distributed transverse loads using displacement and third-order shear deformation theory. The aim of this study is to establish the formula’s for calculation of the critical lateral imposed load of the plate before deflection reaches the specified maximum specified limit q𝑖𝑤 and critical lateral imposed load before plate reaches an elastic yield point q𝑖𝑝. The essence is to ensure that deflection does not exceed specified maximum limit and the plate shear not exceeding the elastic yielding point. Furthermore, this approach overcomes the challenges of the conventional practice in the structural analysis/design which involves checking of deflection and shear; the process which is proved unreliable. Total potential energy equation of a thick plate was formulated from the static elastic theory of the plate. The formulated potential energy was in the same way used by the method of direct variation to obtain the coefficient of deflection and shear deformation. This expression was applied to solve bending problem of two different types of rectangular thick plates. The plates has one edge clamped and other three edges simply supported (CSSS). From the result obtained in this work among the two types of plate, it is observed that the value of q𝑖𝑝 if greater than that of q𝑖𝑤. It can be said that the failure of plate in q𝑖𝑤 is like a warning requesting maintenance whereas failure in q𝑖𝑝 means total failure and cannot be maintained. Hence, failure in deflection (q𝑖𝑤) is seen in the plate into consideration. The numerical analysis obtained, it is found that if the value of critical lateral imposed load (q𝑖𝑤 and q𝑖𝑝) increase as the specified thickness (t) of plate increases and decrease as the length to width ratio increases. This implies that as we increase the thickness and allowable deflection improve the safety in the plate, whereas an increase in the span (length) of the plate increases the failure tendency of the plate structure. Furthermore, effects of aspect ratio of the critical lateral load of isotropic plates are investigated and discussed. It is concluded that the values of critical lateral load obtained by this theory achieve accepted transverse shear stress to the thickness of plate variation and satisfied the transverse flexibility of the condition of the plate while predicting the be characteristics for the CSSS isotropic rectangular thin or thick plate.

scholarly journals An improved shear deformation theory for bending beams with symmetrically varying mechanical properties in the depth direction

2020 ◽  
Vol 231 (10) ◽  
pp. 4381-4395 ◽  
Author(s):  
Krzysztof Magnucki ◽  
Jerzy Lewinski ◽  
Ewa Magnucka-Blandzi
Keyword(s):  
Mechanical Properties ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
The Finite Element Method ◽  
Three Point Bending ◽  
Total Potential ◽  
Depth Direction ◽  
Numerical Studies ◽  
The Individual

Abstract The paper is devoted to simply supported beams under three-point bending. Their mechanical properties symmetrically vary in the depth direction. The individual shear deformation theory for beams of such features is proposed. Based on the principle of stationary total potential energy the differential equations of equilibrium are obtained. The system of the equations is analytically solved, and the shear coefficients and deflections of example beams are calculated. The solution is compared with other analytical results obtained with the use of another deformation function. Moreover, the bending problem of these beams is also numerically studied using the finite element method. Results of analytical and numerical studies are presented in Figures and Tables.

DYNAMIC INSTABILITY OF COMPOSITE SKEW PLATES USING BOUNDARY CHARACTERISTIC ORTHOGONAL POLYNOMIALS

2014 ◽  
Vol 06 (06) ◽  
pp. 1450078 ◽  
Author(s):  
ABHINAV KUMAR ◽  
S. K. PANDA ◽  
RAJESH KUMAR
Keyword(s):  
Potential Energy ◽  
Boundary Conditions ◽  
Total Energy ◽  
Shear Deformation ◽  
Dynamic Instability ◽  
Energy Functional ◽  
Total Potential Energy ◽  
Bending Energy ◽  
Total Potential ◽  
Skew Plate

Dynamic instability analysis of laminated composite skew plate for different skew angles subjected to different type of linearly varying in-plane loadings is investigated. The analysis also includes the instability of skew plate under uniform bi-axial in-plane loading. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is mapped into a square plate over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Different boundary conditions of skew plate have been correctly incorporated by using Rayleigh–Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials (BCOPs). The boundaries of dynamic instability regions are traced by the periodic solution of governing differential equations (Mathieu type equations) with period T and 2T. The width of instability region for uniform loading is higher than various types of linearly varying loadings (keeping the same peak intensity). Effect of various parameters like skew angle, aspect ratio, span-to-thickness ratio, boundary conditions and static load factor on dynamic instability has been investigated.

scholarly journals Application of alternative II theory to vibration and stability analysis of thick rectangular plates (Isotropic and orthotropic)

2020 ◽  
Vol 39 (1) ◽  
pp. 52-62
Author(s):  
O.M. Ibearugbulem ◽  
S.I. Ebirim ◽  
U.C. Anya ◽  
L.O. Ettu
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequency ◽  
Deformation Theory ◽  
Thick Plate ◽  
Shape Function ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
First Order ◽  
Fundamental Natural Frequency

This work analysed the free vibration and stability of thick isotropic and orthotropic plates with SSSS and SSFS support conditions by applying the alternative II theory based on polynomial shape function. The total potential energy which was obtained by combining the strain energy and external work was reduced to three governing equations using Ritz method. Polynomial shape function which varies with Poisson’s ratio was substituted into the governing equation to obtain the fundamental natural frequency, linear frequency and critical buckling load. The values of frequencies of the first mode and critical loads obtained were compared with those obtained using first order shear deformation theory. For span depth ratio of 10, the fundamental linear frequency for orthotropic SSFS plate corresponding to modulus of elasticity ratios (E1/E2) of 10, 25 and 40 are 0.00156, 0.00219 and 0.00255Hz. The corresponding values using first order shear deformation theory are 0.00152, 0.00212 and 0.00245Hz. Keywords: Fundamental natural frequency, SSSS plate, SSFS plate, Ritz method, Orthotropic thick plate, Isotropic thick plate, Stability, Free vibration

BUCKLING ANALYSIS OF TAPERED COMPOSITE PLATES USING RITZ METHOD BASED ON FIRST-ORDER SHEAR DEFORMATION THEORY

2012 ◽  
Vol 12 (04) ◽  
pp. 1250030 ◽  
Author(s):  
SHAIKH AKHLAQUE-E-RASUL ◽  
RAJAMOHAN GANESAN
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Ritz Method ◽  
Turbine Blades ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Width Ratio ◽  
First Order ◽  
Closed Form Analytical Solution

Tapered composite plates have various engineering applications such as helicopter yoke, robot arms and turbine blades in which the structure needs to be stiff at one end and flexible at another end. No closed form analytical solution of tapered composite plates using Ritz method based on first-order shear deformation theory (FSDT) is available at present. In the present paper, the buckling analysis of different types of composite plates with longitudinal-internal-ply-drop-off configuration is investigated using Ritz method. The buckling analysis of these plates is also conducted using ANSYS®. The efficiency and accuracy of the developed formulation are established in comparison with available solutions, where applicable. A detailed parametric study has been conducted on various taper and lay-up configurations, all made of NCT/301 graphite-epoxy, in order to investigate the effects of taper angle, length-to-height ratio, length-to-width ratio, boundary conditions, and taper and lay-up configurations.

A New First-Order Shear Deformation Theory for Free Vibrations of Rectangular Plate

2015 ◽  
Vol 07 (01) ◽  
pp. 1550008 ◽  
Author(s):  
Wei Xiang ◽  
Yufeng Xing
Keyword(s):  
Shear Deformation ◽  
Rectangular Plate ◽  
Deformation Theory ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Present Theory ◽  
Free Vibrations ◽  
Variable Theory ◽  
First Order ◽  
Geometrical Constraints

A new first-order shear deformation theory (FSDT) with pure bending deflection and shearing deflection as two independent variables is presented in this paper for free vibrations of rectangular plate. In this two-variable theory, the shearing deflection is regarded as the only fundamental variable by which the total deflection and bending deflection can be expressed explicitly. In contrast with the conventional three-variable first-order shear plate theory, present variationally consistent theory derived by using Hamiltonian variational principle can uniquely define the bending and the shearing deflections, and give two rotations by the differentiations of bending deflection. Due to more restrictive geometrical constraints on rotations and boundary conditions, the obtained natural frequencies are equal to or higher than those by conventional FSDT for the rectangular plate with at least one pair of opposite edges simply supported. This new theory is of considerable significance in theoretical sense for giving a simple two-variable FSDT which is variational consistent and involve rotary inertia and shear deformation. The relation and differences of present theory with conventional FSDT and other relative formulations are discussed in detail.

A powerful numerical approach for the axisymmetric bending response of shear deformable two-directional functionally graded (2D-FG) plates with variable thickness

2021 ◽  
pp. 095440622110108
Author(s):  
Ahmad Reshad Noori ◽  
Beytullah Temel
Keyword(s):  
Shear Deformation ◽  
Variable Thickness ◽  
Shear Deformation Theory ◽  
Numerical Approach ◽  
Functionally Graded ◽  
Total Potential ◽  
Fg Plates ◽  
Wide Range ◽  
Axisymmetric Bending ◽  
Bending Response

In the present article, a powerful numerical approach is applied to the axisymmetric bending of 2 D-FG circular and annular plates with variable thickness. The mechanical properties of the materials of the plate are assumed to vary continuously both in the radial and thickness directions. The principle of minimum total potential energy is used to obtain the governing equations. Shear deformation is considered based on the first-order shear deformation theory (FSDT). These ODEs are solved via the Complementary Functions Method (CFM) for the first time. The novelty of this paper is the infusion of the CFM to the axisymmetric bending of a wide range of annular or circular plates, with variable thickness, radially FG (RFG), FG in thickness direction, or 2D-FG. In addition to adopting this effective numerical approach to the present class of problems, various parametric studies are presented to show the influence of material variation parameters and geometric constants on the axisymmetric bending response of the considered structures. Results of the proposed approach are validated with those carried out by FEM and those of the available published literature. An excellent agreement is observed.

Sign in / Sign up

Export Citation Format

Share Document