A Method for Analyzing Elastic Large Deflection Behavior of Perfect and Imperfect Plates With Partially Rotation-Restrained Edges

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Jeom Kee Paik ◽  
Do Kyun Kim ◽  
Hoseong Lee ◽  
Yong Lae Shim
Keyword(s):  
Large Deflection ◽  
Biaxial Loading ◽  
Torsional Rigidity ◽  
Nonlinear Behavior ◽  
Edge Condition ◽  
Biaxial Compression ◽  
Buckling Behavior ◽  
Deflection Analysis ◽  
Post Buckling ◽  
Loading Ratio

The edge condition of the plating in a continuous stiffened-plate structure is neither simply supported nor clamped because the torsional rigidity of the support members at the plate edges is neither zero nor infinite. In a robust ship structural design, it is necessary to accurately take into account the effect of the edge condition in analyses of plate behavior in terms of buckling and post-buckling behavior. The aim of this study is to develop a new method for analyzing the geometric nonlinear behavior (i.e., elastic large deflection or post-buckling behavior) of plates with partially rotation-restrained edges in association with the torsional rigidity of the support members and under biaxial compression. An analytical method was developed to solve this problem using the nonlinear governing differential equations of plates. The validity of the developed method was confirmed by comparison with nonlinear finite element method solutions with varying values for the torsional rigidity of the support members, plate aspect ratio, and biaxial loading ratio. The developed method was found to give reasonably accurate results for practical design purpose in terms of the large deflection analysis of plates with partially rotation-restrained edges, and it will be useful for the robust design of ship structures in association with buckling and ultimate strength of plates surrounded by support members.

Elastic Large Deflection Behavior of Plates With Partially Rotation-Restrained Edges

2010 ◽  
Author(s):  
Jeom Kee Paik ◽  
Do Kyun Kim ◽  
Hoseong Lee ◽  
Yong Lae Shim
Keyword(s):  
Structural Design ◽  
Large Deflection ◽  
Biaxial Loading ◽  
Torsional Rigidity ◽  
Edge Condition ◽  
Biaxial Compression ◽  
Nonlinear Finite Element Method ◽  
Deflection Analysis ◽  
Loading Ratio ◽  
Plate Aspect Ratio

The edge condition of the plating in a continuous stiffened-plate structure is neither simply supported nor clamped because the torsional rigidity of the support members at the plate edges is neither zero nor infinite. In a robust ship structural design, it is necessary to accurately take into account the effect of the edge condition in analyses of plate behavior. The aim of this study is to investigate the elastic large deflection behavior of plates with partially rotation-restrained edges in association with the torsional rigidity of the support members and under biaxial compression. An analytical method was developed to solve this problem using the nonlinear governing differential equations of plates. The validity of the developed method was confirmed by the comparison with nonlinear finite element method solutions with varying values for the torsional rigidity of the support members, plate aspect ratio, and biaxial loading ratio. The developed method was found to give very accurate results for the large deflection analysis of plates with partially rotation-restrained edges, and was proved very useful for the robust design of ship structures.

Post-Buckling of Piezoelectric Thin Plates

2015 ◽  
Vol 15 (07) ◽  
pp. 1540020 ◽  
Author(s):  
Michael Krommer ◽  
Hans Irschik
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Nonlinear Behavior ◽  
Dirichlet Boundary Conditions ◽  
Thin Plates ◽  
Governing Equations ◽  
Simply Supported ◽  
Buckling Behavior ◽  
Single Term ◽  
Post Buckling ◽  
Special Case

In the present paper, the geometrically nonlinear behavior of piezoelastic thin plates is studied. First, the governing equations for the electromechanically coupled problem are derived based on the von Karman–Tsien kinematic assumption. Here, the Berger approximation is extended to the coupled piezoelastic problem. The general equations are then reduced to a single nonlinear partial differential equation for the special case of simply supported polygonal edges. The nonlinear equations are approximated by using a problem-oriented Ritz Ansatz in combination with a Galerkin procedure. Based on the resulting equations the buckling and post-buckling behavior of a polygonal simply supported plate is studied in a nondimensional form, where the special geometry of the polygonal plate enters via the eigenvalues of a Helmholtz problem with Dirichlet boundary conditions. Single term as well as multi-term solutions are discussed including the effects of piezoelectric actuation and transverse force loadings upon the solution. Novel results concerning the buckling, snap through and snap buckling behavior are presented.

Large-deflection and post-buckling behavior of slender beam-columns with non-linear end-restraints

2011 ◽  
Vol 46 (1) ◽  
pp. 79-95 ◽  
Author(s):  
Carlos Vega-Posada ◽  
Mauricio Areiza-Hurtado ◽  
J. Dario Aristizabal-Ochoa
Keyword(s):  
Large Deflection ◽  
Beam Columns ◽  
Buckling Behavior ◽  
Non Linear ◽  
Post Buckling

Ultimate Capacity Behavior of Pitted Mild Steel Plates Under Biaxial Compression

2011 ◽  
Author(s):  
Xiaoli Jiang ◽  
C. Guedes Soares
Keyword(s):  
Mild Steel ◽  
Biaxial Loading ◽  
Fem Analysis ◽  
Steel Plates ◽  
Dominant Factor ◽  
Biaxial Compression ◽  
Ultimate Capacity ◽  
Thickness Loss ◽  
Loading Ratio ◽  
Corrosion Pits

The aim of the present paper is to investigate the effects of corrosion pits on the ultimate capacity of rectangular mild steel plates under biaxial compression. A series of non-linear FEM analysis on plates with partial depth pits are carried out, changing geometrical attributes of both pits and plates, i.e., the radius, depth, location and distribution of the pits and the slenderness of the plates. Possible interaction between transverse and longitudinal axial compression is studied applying different level of loading ratio and considering the effects of partial depth pitting corrosion. It is shown that biaxial loading ratio is a dominant factor affecting the behavior of pitted plates besides pits intensity and thickness loss at pits. When longitudinal compression is dominant load with loading ratio lower than 1, the interaction relationship curves for different DOP levels tend to be parallel with each other and the distance between every two parallel curves seems to be dependent mainly on the deviation of their DOP values and thickness loss at pits. Moreover, pits distribution along long and shirt edges could also affect the ultimate strength behavior of plates. The work done in the paper illustrates that the ultimate capacity of pitted plate could be derived from intact plate by introducing important influential parameters like DOP, thickness loss and possible pits distribution.

Post-buckling and Snap-Through Behavior of Inclined Slender Beams

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Jian Zhao ◽  
Jianyuan Jia ◽  
Xiaoping He ◽  
Hongxi Wang
Keyword(s):  
Large Deflection ◽  
Buckling Modes ◽  
Strongly Nonlinear ◽  
Elastic Beams ◽  
Buckling Behavior ◽  
Geometrical Nonlinear ◽  
Slender Beams ◽  
Post Buckling ◽  
Inclined Beam ◽  
Good Agreement

Based on the geometrical nonlinear theory of large deflection elastic beams, the governing differential equations of post-buckling behavior of clamped-clamped inclined beams subjected to combined forces are established. By using the implicit compatibility conditions to solve the nonlinear statically indeterminate problems of elastic beams, the strongly nonlinear equations formulated in terms of elliptic integrals are directly solved in the numerical sense. When the applied force exceeds the critical value, the numerical simulation shows that the inclined beam snaps to the other equilibrium position automatically. It is in the snap-through process that the accurate configurations of the post-buckling inclined beam with different angles are presented, and it is found that the nonlinear stiffness decreases as the midpoint displacement is increased according to our systematical analysis of the inward relations of different buckling modes. The numerical results are in good agreement with those obtained in the experiments.

Nonlinear Static and Dynamic Analysis of Space Frames with Semi-Rigid Connections

1993 ◽  
Vol 8 (4) ◽  
pp. 261-269 ◽  
Author(s):  
Siu Lai Chan
Keyword(s):  
Dynamic Analysis ◽  
Large Deflection ◽  
Numerical Procedure ◽  
Computational Effort ◽  
Joint Orientation ◽  
Static And Dynamic Analysis ◽  
Space Frames ◽  
Orientation Method ◽  
Deflection Analysis ◽  
Post Buckling

To obtain an accurate insight into the behaviour of frames, joint flexibility must be accounted for in an analysis since most connections are neither fully rigid nor frictionless pinned but semi-rigid. A robust numerical procedure for large deflection static and dynamic analysis of frames with semirigid connections is presented in this paper. The method is consistent in handling both the static and dynamic problems and its programming and computational effort is moderate when compared to the currently available techniques for large deflection analysis such as the joint orientation method. The pre- and post- buckling static load versus deflection paths for flexibly jointed space frames are traced. The behaviour of some commonly studied problems is re-analysed statically and dynamically using the semi-rigid joint assumption in order to demonstrate the importance of considering connection flexibility in a nonlinear analysis.

Elastic-Plastic Analysis and Research of Large Profiled Structure under Rare Strong Earthquakes Based on FNA Method

2013 ◽  
Vol 838-841 ◽  
pp. 1556-1561
Author(s):  
Na Xie ◽  
Gan Wang ◽  
Jian Zhong Zhao ◽  
Zhi Ming Zhao ◽  
Hui Xin Zhou ◽  
...  
Keyword(s):  
Seismic Design ◽  
Nonlinear Behavior ◽  
Steel Structure ◽  
Steel Structures ◽  
Strong Earthquakes ◽  
Design Goal ◽  
Buckling Behavior ◽  
Plastic Analysis ◽  
Post Buckling ◽  
Internal Forces

In rare strong earthquakes, the steel structure may occur the nonlinear behavior and redistribution of internal forces. In order to understand the post-buckling behavior of steel structures and determine the weak areas of the structure, and then determine whether the structure under strong earthquakes meets the seismic design goal or not, this paper adopts the FNA method to analyze the response of large profiled steel structure under severe earthquakes. Finally, we draw some general conclusions which are valuable for designing the large profiled structure.

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