scholarly journals A Contribution to Analytical Solutions for Buckling Analysis of Axially Compressed Rectangular Stiffened Panels

2021 ◽  
Vol 31 (5) ◽  
pp. 301-306
Author(s):  
Victor Tochukwu Ibeabuchi ◽  
Mathias Owus Ibearugbulem ◽  
Kelechi Okechukwu Njoku ◽  
Ezekiel Onyinyechi Ihemegbulem ◽  
Princewill Obumneke Okorie
Keyword(s):  
Energy Functional ◽  
Stiffened Panel ◽  
Computationally Efficient ◽  
Numerical Accuracy ◽  
Stiffened Panels ◽  
Total Potential ◽  
Deflection Coefficient ◽  
Edge Conditions ◽  
Compressive Loads ◽  
Potential Energy Functional

Analytical solution to the buckling problems of stiffened panels subjected to in-plane compressive loads is presented. The total potential energy functional of stiffened panel is obtained by the summation of that of a line continuum and stiffened panel derived from elastic principles of mechanics. Minimizing the resulting equation with respect to deflection coefficient and rearranging gives the expression for obtaining the buckling load of stiffened panel. Exact deflection functions were substituted directly in the new solution and various edge conditions were considered in this analysis. Obtained results were compared with analytical results of previous works. The method is computationally efficient for complex edge conditions and gives high numerical accuracy.

Effective Breadth Problems by an Eigenfunction Approach

1987 ◽  
Vol 31 (04) ◽  
pp. 217-226
Author(s):  
Subroto Kumar BhaHacharyya ◽  
Chiruvai P. Vendhan
Keyword(s):  
Shear Stress ◽  
Alternative Form ◽  
Normal Displacement ◽  
Tangential Displacement ◽  
Stiffened Panel ◽  
Stiffened Panels ◽  
Plane Stress Problem ◽  
Edge Conditions ◽  
Support Conditions ◽  
First Time

The problem of effective breadth of a stiffened panel with two different edge or support conditions, namely (i) stres -free ed es and (ii) displacement restrained edges, has been solved for the first time, in this paper, by the e.• enfunctoon approach o the end problem of semi-infinite strips. It is shown that these two edge condollens lead to complex eogenvalue problems and thus the plane-stress problem of the plating cannot be solved by the classical methods which have been hitherto successfully used to obtain the estimates of effective breadths for the two other possible mixed edge conditions, namely, (i) vanishing direct stress and tangential displacement and (ii) vanishing normal displacement and shear stress. It is brought out that this end eigenlunetion formulation, using a generalized orthogonality of Papkovich, provides a general analytical framewerk for the stress field problems of stiffened panels in bending. Numerical results are presented for the first problem nly. The two classical problems have been revisited from this viewpoint, and certain well-known effectove breadth results have been rederived and compared. An alternative form of the generalized orthogonality relation, which offers a certain analytical advantage, has been used and the exostence of such a form is proved for all four edge conditions.

Analysis of Orthotropic Thin Rectangular Simply Supported Plate Subjected to both In-Plane Compression and Lateral Loads

2020 ◽  
Vol 48 ◽  
pp. 63-77
Author(s):  
D.O. Onwuka ◽  
O.M. Ibearugbulem ◽  
Duke Bertram
Keyword(s):  
Yield Strength ◽  
Potential Energy ◽  
Elastic Stability ◽  
Lateral Load ◽  
Energy Functional ◽  
Total Potential Energy ◽  
Lateral Loads ◽  
Total Potential ◽  
Plane Compression ◽  
Potential Energy Functional

This study presents the analysis of thin rectangular orthotropic plate, simply supported at all edges (SSSS) subjected to both in-plane compression and lateral loads. The total potential energy functional was used in the analysis. The general variation of the total potential energy functional was done and the governing equation was obtained. The solution of the direct integration of the governing equation gave the deflection of the plate as a product of the coefficient of deflection and an orthogonal polynomial shape function. The expression for the coefficient of deflection was obtained by the direct variation of the total potential energy functional. This was used to derive the equation for the Lateral load parameter of an orthotropic thin rectangular plate carrying both in-plane compression and lateral loads based on the maximum deflection condition and also based on the elastic stability (yield strength) condition. The peculiar deflection equation for the SSSS plate was obtained using the formulated polynomial shape function. Numerical examples were carried out to determine the lateral load parameters corresponding to various plate thickness and permissible deflection for orthotropic thin SSSS plate carrying both in-plane compression and lateral load. In the same way, the lateral load parameters using the elastic stability condition (yield strength) were obtained for yield strength of 275 MPa, 355 MPa and 410 MPa

scholarly journals Analytical Study of Bending Characteristics of an Elastic Rectangular Plate using Direct Variational Energy Approach with Trigonometric Function

2021 ◽  
Vol 5 (6) ◽  
pp. 916-928
Author(s):  
F. C. Onyeka ◽  
B. O. Mama
Keyword(s):  
Deformation Theory ◽  
Thick Plate ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Energy Functional ◽  
Total Potential Energy ◽  
Total Potential ◽  
Plate Analysis ◽  
Potential Energy Functional

In this paper, an analytical three-dimensional (3D) bending characteristic of an isotropic rectangular thick plate with all edges simply supported (SSSS) and carrying uniformly distributed transverse load using the energy technique is presented. The three-dimensional constitutive relations which involves six stress components were used in the established, refined shear deformation theory to obtain a total potential energy functional. This theory obviates application of the shear correction factors for the solution to the problem. The governing equation of a thick plate was obtained by minimizing the total potential energy functional with respect to the out of plane displacement. The deflection functions which are in form of trigonometric were obtained as the solution of the governing equation. These deflection functions which are the product of the coefficient of deflection and shape function of the plate were substituted back into the energy functional, thereafter a realistic formula for calculating the deflection and stresses were obtained through minimizations with respect to the rotations and deflection coefficients. The values of the deflections and stresses obtained herein were tabulated and compared with those of previous 3D plate theory, refined plate theories and, classical plate theory (CPT) accordingly. It was observed that the result obtained herein varied more with those of CPT and RPT by 25.39% and 21.09% for all span-to-thickness ratios respectively. Meanwhile, the recorded percentage differences are as close as 7.17% for all span-to-thickness ratios, when compared with three dimensional plate analysis. This showed that exact 3D plate theory is more reliable than the shear deformation theory which are quite coarse for thick plate analysis. Doi: 10.28991/esj-2021-01320 Full Text: PDF

Local Buckling of Stiffeners in Ship Plating

1998 ◽  
Vol 42 (01) ◽  
pp. 56-67 ◽  
Author(s):  
Jeom Kee Paik ◽  
Anil K. Thayamballi ◽  
Young Eel Park
Keyword(s):  
Local Buckling ◽  
Stiffened Panel ◽  
Stiffened Panels ◽  
Buckling Strength ◽  
Compressive Loads ◽  
Governing Differential Equation ◽  
Web Buckling ◽  
Buckling Coefficient ◽  
Approximate Expressions ◽  
Basic Investigation

The aim of the present study is to analytically investigate the characteristics of local buckling of the stiffener web in the stiffened panels under uniaxial compressive loads. A plate-stiffener combination model is used as representative of the stiffened panel. The elastic buckling condition for the stiffener web is analytically derived by solving the characteristic value problem involving the governing differential equation under the corresponding loading and boundary conditions. A series of analyses of stiffener web buckling strength for varying proportions of plating and web/flange is carried out. Based on the computed results, a basic investigation of stiffener web buckling is made. Closed-form approximate expressions for predicting the buckling strength of the stiffener web are derived taking into account the influence of rotational restraints at the plate-stiffener web connection and stiffener web-flange intersections. Design considerations for potentially preventing buckling of the stiffener web are then discussed. The computed basic results for the stiffener web buckling coefficient are documented.

Reliability-Based Specification of Welding Distortion Tolerances for Stiffened Steel Panels

2003 ◽  
Vol 47 (01) ◽  
pp. 39-47
Author(s):  
Tarek Elsayed ◽  
Alaa Mansour
Keyword(s):  
Slenderness Ratio ◽  
Simple Expression ◽  
Welding Distortion ◽  
Stiffened Panel ◽  
Ship Structures ◽  
Design Guideline ◽  
Stiffened Panels ◽  
Compressive Loads ◽  
Accurate Expression ◽  
Steel Panels

The purpose of this study is to analytically derive a simple and reasonably accurate expression for the maximum allowable unfairness tolerance of longitudinally stiffened panels in ship structures. The stiffened panels under consideration are typical of those found in the deck, bottom, or side shell of longitudinally stiffened ships. They are assumed to be under still water and wave-induced loads, resulting in predominantly compressive loads. A plate-stiffener combination model is used as representative of the stiffened panel. Ultimate strength is determined based on a strut approach taking into account the effects of initial stiffener deflection and welding residual stresses in the stiffener. A series of stiffener reliability analyses relative to the ultimate failure strength of the stiffener for varying proportions of column slenderness ratios is carried out. Based on the computed results, a simple expression for predicting the maximum allowable unfairness tolerance of the stiffener is derived. The developed expression, expressed in terms of the stiffener slenderness ratio, can be useful for the assessment of fairness limits of plating with frames, or as a design guideline in ship structures during construction.

Ultimate Strength of Stiffened Plates Subjected to Longitudinal Compression and Lateral Pressure

2014 ◽  
Author(s):  
Karan Doshi ◽  
Suhas Vhanmane
Keyword(s):  
Finite Element ◽  
Ultimate Strength ◽  
Lateral Pressure ◽  
Stiffened Plates ◽  
Stiffened Panel ◽  
Element Analysis ◽  
Stiffened Panels ◽  
Linear Finite Element ◽  
Non Linear ◽  
Compressive Loads

This paper presents a non-linear finite element analysis (FEA) and subsequent formula development for ultimate strength of stiffened panels of ship structures. A review of studies on ultimate strength of ship plating subjected to lateral pressure was carried out. The present work takes into account, the influence due to the lateral pressure on the ultimate strength of stiffened plates with initial imperfections subject to longitudinal compressive loads. ANSYS non-linear FE software was used for non linear finite element analyses of stiffened panels (864 cases) considering VLCC hull. Based on regression analysis, a set of semi-analytical formulae were proposed and described. It is observed that depending upon the failure mode, scantlings of the stiffened panel and magnitude of lateral pressure, ultimate strength of the stiffened panels in compression is affected.

scholarly journals Effects of plies orientations and initial geometric imperfections on buckling strength of a composite stiffened panel

2018 ◽  
Vol 191 ◽  
pp. 00008
Author(s):  
Ikram Feddal ◽  
Abdellatif Khamlichi ◽  
Koutaiba Ameziane
Keyword(s):  
Stiffened Panel ◽  
Buckling Mode ◽  
Element Analysis ◽  
Geometric Imperfections ◽  
Stiffened Panels ◽  
Specific Strength ◽  
Euler Buckling ◽  
Buckling Behavior ◽  
Composite Stiffened Panel ◽  
Strength And Stiffness

The use of composite stiffened panels is common in several activities such as aerospace, marine and civil engineering. The biggest advantage of the composite materials is their high specific strength and stiffness ratios, coupled with weight reduction compared to conventional materials. However, any structural system may reach its limit and buckle under extreme circumstances by a progressive local failure of components. Moreover, stiffened panels are usually assembled from elementary parts. This affects the geometric as well as the material properties resulting in a considerable sensitivity to buckling phenomenon. In this work, the buckling behavior of a composite stiffened panel made from carbon Epoxy Prepregs is studied by using the finite element analysis under Abaqus software package. Different plies orientations sets were considered. The initial distributed geometric imperfections were modeled by means of the first Euler buckling mode. The nonlinear Riks method of analysis provided by Abaqus was applied. This method enables to predict more consistently unstable geometrically nonlinear induced collapse of a structure by detecting potential limit points during the loading history. It was found that plies orientations of the composite and the presence of geometric imperfections have huge influence on the strength resistance.

scholarly journals The Prediction of Buckling Load of Laminated Composite Hat-Stiffened Panels Under Compressive Loading by Using of Neural Networks

2018 ◽  
Vol 12 (1) ◽  
pp. 468-480 ◽  
Author(s):  
Shashi Kumar ◽  
Rajesh Kumar ◽  
Sasankasekhar Mandal ◽  
Atul K. Rahul
Keyword(s):  
Neural Network ◽  
Finite Element ◽  
Network Architecture ◽  
Laminated Composite ◽  
Buckling Load ◽  
Stiffened Panel ◽  
Stiffness Ratio ◽  
Data Set ◽  
Stiffened Panels ◽  
Structural Problems

Background:Stiffened panels are being used as a lightweight structure in aerospace, marine engineering and retrofitting of building and bridge structure. In this paper, two efficient analytical computational tools, namely, Finite Element Analysis (FEA) and Artificial Neural Network (ANN) are used to analyze and compare the results of the laminated composite 750-hat-stiffened panels.Objective:Finite Element (FE) is an efficient and versatile method for the analysis of a complex problem. FE models have been used to generate data set of four different parameters. The four parameters are extensional stiffness ratio of skin in the longitudinal direction to the transverse direction, orthotropy ratio of the panel, the ratio of twisting stiffness to transverse flexural stiffness and smeared extensional stiffness ratio of stiffeners to that of the plate.Results and Conclusion:For training of ANN, multilayer feedforward back-propagation has been used as a network function with two-hidden layers in the neural network. The good network architecture is achieved after several iterations to predict the buckling load of the stiffened panel. ANN prediction for unknown new data set is in good agreement with FEA results of different cases, which show that ANN tool can be used for the design of complex structural problems in civil engineering and optimization of the laminated composite stiffened panel.

Finite Element Analysis of Top-Hat–Stiffened Panels of Fiber-Reinforced–Plastic Boat Structures

2007 ◽  
Vol 44 (01) ◽  
pp. 16-26
Author(s):  
Ömer Eksik ◽  
R. Ajit Shenoi ◽  
Stuart S. J. Moy ◽  
Han Koo Jeong
Keyword(s):  
Finite Element ◽  
Lateral Pressure ◽  
Three Dimensional ◽  
Element Model ◽  
Stiffened Panel ◽  
Element Analysis ◽  
Stiffened Panels ◽  
Fiber Reinforced Plastic ◽  
Reinforced Plastic ◽  
Experimental Findings

This paper describes the development of a finite element model in order to assess the static response of a top-hat-stiffened panel under uniform lateral pressure. Systematic calculations were performed for deflection, strain, and stress using the developed model based on the ANSYS three-dimensional solid element (SOLID45). The numerical modeling results were compared to the experimental findings for validation and to further understand an internal stress pattern within the different constituents of the panel for explaining the likely causes of the panel failure. Good correlation between experimental and numerical strains and displacements was achieved.

Boundary Perturbations due to the Presence of Small Cracks

2015 ◽  
Author(s):  
Habib Ammari ◽  
Elie Bretin ◽  
Josselin Garnier ◽  
Hyeonbae Kang ◽  
Hyundae Lee ◽  
...  
Keyword(s):  
Asymptotic Formula ◽  
Neumann Boundary ◽  
Representation Formula ◽  
Fundamental Solutions ◽  
Energy Functional ◽  
Finite Hilbert Transform ◽  
Time Harmonic ◽  
Elastic Potential Energy ◽  
Potential Energy Functional ◽  
Boundary Perturbations

This chapter considers the perturbations of the displacement (or traction) vector that are due to the presence of a small crack with homogeneous Neumann boundary conditions in an elastic medium. It derives an asymptotic formula for the boundary perturbations of the displacement as the length of the crack tends to zero. Using analytical results for the finite Hilbert transform, the chapter derives an asymptotic expansion of the effect of a small Neumann crack on the boundary values of the solution. It also derives the topological derivative of the elastic potential energy functional and proves a useful representation formula for the Kelvin matrix of the fundamental solutions of Lamé system. Finally, it gives an asymptotic formula for the effect of a small linear crack in the time-harmonic regime.

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