I.                    INTRODUCTION

A.                 OBJECTIVE

The objective of this work is to put forward an analysis and comparison of buckling behaviour of two stiffened plate of different geometrical property with one plate having square junction to the stiffener and the other having filleted junction to the stiffener. Eigen buckling analysis through ANSYS mechanical apdl software was chosen be used. The deflection and different stress values of the stiffened plate were compared for conclusion. Additionally, the concept of parameters influencing the behaviour and strength of the stiffened plates were taken into consideration and hence the influence of the aspect ratio parameter on the ultimate strength of the stiffened plate and the influence of the slenderness ratio parameter on the failure modes were analysed for conclusion.

B.                  BACKGROUND

A structure which is safe in deflection and normal stress, fails in buckling. Plates are widely used in the structure which is subjected to continues loading throughout their life span. To withstand such a load, stiffeners are introduced which increases the strength, the overall stiffness and provide resistance to buckling. Plates are available in various forms such as rectangular, skew, and curve. These are different types of stiffener system, namely transverse, longitudinal and both transverse and longitudinal system. In this work, rectangular plates with longitudinal stiffener system was used.

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The stiffened plate is one of the most basic component among all which is identified in bridges, buildings, airplanes, offshore structures. The main difference between the offshore structures and other structure is that the former one experiences In-plane loads in addition to the other loads. Due to their complexity in the structure, the concept of elastic instability has to studied well to proceed further. To understand the behaviour of the stiffened plate in such loading, buckling analysis is done. Basically, three forms of procedure namely theoretical and/or numerical computer-aided and/or experimental can be adopted. In this work, numerical computer aided approach along with theoretical validation was adopted. The most common computer aided programming of Finite Element Analysis- ANSYS was used.

According to the load and the behaviour, the modes of buckling differs namely local buckling, overall buckling, and tripping. The main criteria to prevent the failure was to reduce the overall buckling by confining the plate within local buckling which will increase the stiffness of the plate.

The buckling performance can be influenced by variation in cross section, which suits the case of stiffened plate with filleted junction. Larger the radius of the fillet, the weight of the whole plate structure increases. Hence the geometry of the plate influences the buckling. In such a case, the fillet radii are an important parameter.

Numerical results for both the plate are obtained through Finite Element Program software ANSYS and compared for the conclusion.

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C.                  NEED FOR RESEARCH

The plates in the ship deck are subjected to continuous loading and are prone to buckling. In such a case, the concept of increasing the thickness or providing the stiffeners to the plate are implemented which will increase the stiffness. On the other hand, stiffened plate on a particular zone can also experience buckling due to heavy loading by which the introduction of additional structure such a filleted junction to the stiffened plate can increase the stiffness. This work is important in analysing, comparing both the plates and the previous works identified rarely used ANSYS software for simulation by which this work become unique. Additionally, it is important to understand the behaviour of the stiffened plate on different environmental condition which lies in proportion with two important parameters such as aspect ratio and slenderness ratio. Hence, this work proves to be important for all the structural engineers.

D.                 LITERATURE REVIEW

Razzaque and M. D. Mathers (A. Razzaque & M. D. Mathers, 1983), conducted various experiments on buckling analysis of stiffened plates and shells. Ali Rezo Poladkhan et al (Ali Rezo Pouladkhan, et al., 2011), presented a paper in which they used equilibrium equation to analyse the buckling of stiffened plates. Archie Wilmer III (Archie Wilmer III, 2003), presented a paper on buckling analysis of plates with bulb flat flange stiffener and concluded that the former is four percent less than the T-flange stiffener. Ashutosh kumar, Rachayya R. Arakerimath (Ashutosh Kumar & Rachayya R. Arakerimath, 2015), analytically derived the buckling mode shapes, the nature of buckling using equilibrium method and compared it with finite element approach which was found to be matching. Dr. Alice Mathai et al (Dr. Alice Mathai, et al., 2014), presented a non-linear buckling analysis of stiffened plate and compared it with finite element software NISA which was found to be convincing. Ghania Ikhenazen, Messaoud Saidani (Ghania Ikhazen & Messaoud Saidani, 2010), used total energy concept to analyse the chart of buckling factor versus aspect ratio and width ratio of an isotropic plate subjected to in-plane loading. J.Rhodes (J. Rhodes, 2002), presented paper on buckling analysis of stiffened plates subjected to local buckling. He also concluded that the confining the plate to maximum local buckling wuld prevent the overall buckling. Mudhujit Mukhopadhayay, Abjijit Mukherjee (Mudhujit Mukhopadhay & Abhijit mukherjee, 1990), carried out numerical analysis on stiffened iso-parametric and skew plate. He concluded that the stiffener can accommodate irregular boundaries and the buckling load reduces with eccentricity of the stiffeners. P. Seide (P. Seide, 1953), derived the effective moment of inertia from the effect of eccentricity of the stiffeners. Patrick E. Fenner, Andrew Watson (Patrick E. Fenner & Andrew Watson, 2012), presented a work on buckling analysis of stiffened plate with filleted junction. He came up with a conclusion that there is limit of adding mass at junctions to increase the local buckling stability. The fillet increases the stiffness however it also increases the critical buckling stress. He also suggested that a higher fillet size increases the value of K than the upper bound value.

II.                  CHARACTERISTICS OF FINITE ELEMENT METHODS

A.                 BUCKLING MODES OF STIFFENED PLATES

The failure of the stiffened plate can be in different forms namely local buckling, plate induced failure or stiffener induced failure overall buckling and tripping. Theoretically, the local and overall failure can be identified in all wavelengths but practically it is difficult due to the material strength at that point.

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In the local mode of failure, the web line junction does not project to the out-of-plane direction but in some cases there exists where the line junction exits the out-of-plane area. This displacement will be small such like (1/10) ^th of the overall displacement which strengthens the fact that it does not project to the out-of-plane area. In this work, the stiffened plate which is subjected to uniaxial edge compression is adopted which allows to perform theoretical calculation and analysis around the overall or tripping failure.

In the case of overall buckling of plates, the web line junction exceeds the out-of-plane point which means the plate does not lie straight. The projection of the line junction will be in the form of half wave which looks similar to half sine wave. The overall buckling which is also referred as Euler type buckling is simultaneous failure of both plate and stiffener. If the failure takes place with stiffener on the tension side, then it is referred as plate induced overall buckling. On the other hand, if the failure is due to stiffener being on the compression side then it is referred as stiffener induced overall buckling.

Tripping failure of stiffened plate is lateral torsional buckling which takes place about the stiffener to plate junction (Imtiaz A. Sheikh, et al., 2001). It is actually sudden drop in load carrying capacity. This type of failure can be serious at times due to the drop in load carrying capacity. It has to be noted that the tripping stiffener experience tension but it may also be subjected to compression due to bending.

B.                  WELDING CHARACTERISTICS AND TECHNIQUES IN SHIP PLATES

Welding of ships plates and the stiffener are carried out in two different ways. Continuous welding is used as a procedure to weld the plate and the stiffener which requires huge quantity of weld. It may also add to the weight of the ship and increases the construction cost. Despite increasing the welding quantity, this procedure becomes faster and reduces the labour cost.

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Alternatively, the longitudinal stiffeners are attached to plating using intermittent fillet welds. This process reduces the construction cost and also the amount of residual stresses when compared to the former welding process.

Welding the stiffener plates affects both initial distortion and the residual stresses. These two parameter can vary and number of statistical work has been done in understanding this concept by experts.

Faulkner (1975), Carlsen and Czujko (1978) and Smith et al. (1991), conducted surveys on different structures to assess the above two parameters. Faulkner (1975) assessed 300 built in stiffened plates specimens and measured the initial plate distortion. He proposed a relationship for

table shows the dimensions of the square stiffened plate, load applied to solve the same.

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Table dimensions of square stiffened plate and load applied

Figure Geometry of square stiffened plate

Figure: Nodal Geometry of the square stiffened plate with boundary condition

To compare the behaviour of square stiffened plate, stiffened plate with filleted junctions was solved. The process of solving this plate involved designing of the stiffened plate which was as same as square stiffened plate but the only difference was the addition of the fillet junction between the plate and the stiffener. As mentioned in chapter I.B, fillet radii is an important criteria in these cases, it was decided to use four different radii’s of 2mm, 3mm, 4mm, 5mm respectively. Since welding technique for fillet was adopted for the connection of plate and stiffener, the influence of residual stresses was taken into consideration. The residual stresses were calculated from the equation. The residual stresses were applied initially on the fillet junction to allow for the initial deflection. Furthermore, external load was applied in the longitudinal direction of the plate to calculate the deflection, von mises stress and load factor values for respective fillet radii stiffened plates and finally the ultimate strength of the plate was calculated. The table shows the dimensions of the stiffened plate along with the fillet radii and the residual stresses calculated from the equation.

Table Dimension of the stiffened plate with fillet radii and residual stresses

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Figure View of part of stiffened plate with filleted junction

Figure Full view of stiffened plate with filleted junction

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Figure Nodal geometry of the filleted junction stiffened plate with boundary conditions

Figure Mapped meshing of the stiffened plate with filleted junction

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IV.               RESULTS

A.                 EFFECT OF SLENDERNESS PARAMETER ON FAILURE MODE

The simulation of different slenderness parameter stiffened plate carried out through ansys were observed. The progressive mode of the failure of the stiffened plate subjected to unit compressive load was also observed and three different modes of failure was identified. Those modes were plate induced failure, plate buckling and dual failure. All the three different parameter β₁, β₂, β₃ had their respective influences on the strength and the behaviour of the plate. For the different slenderness ratio stiffened plate, the load factor value is obtained through the software and the ultimate strength is calculated by multiplying the factor with the length of the plate. From the obtained ultimate strength, plots were created for better understanding. The plots were created with the slenderness parameter and the ultimate strength of the plate. Also, the relation between the slenderness parameters and the failure mode was also understood with the help of the table. The pictures help to come forward with the future work and a conclusion of the influence of this parameter on the ultimate strength.

Table () Effect of β₁ with β₃ = 0.3 on plates with uniaxial compression

Table () Effect of β2 with β₃ = 0.3 on plates with uniaxial compression

Table () Effect of β₃ on plates with uniaxial compression

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Effect of β₁ on P when β₂ =0.5

Effect of β₁ on P when β₂ =1

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