Dynamic effects of a mass falling on a reinforced rectangular plate

Lect. Dr. Mazin Y. Abood

College of Engineering / University of Anbar

Introduction:

The plate is said to be thin if its thickness is no larger than one-tenth of the length of the smallest lateral dimension. For a given loading, the stiffness of a plate or shell structure can be increased significantly by adding the ribs or stiffeners. Previously, the optimization techniques are mainly on the sizing of the ribs. The more important issue of identifying the optimum location of the ribs has received little attention. Impact on flexible structures is a complex phenomenon which includes the interaction between the projectile and the structure, the response of the structure and the response of the projectile. A complete modeling of an impact event can always be done using a 3D Finite Element model. This method involves the consideration of the contact between the impacting bodies, increasing the time required for numerical simulation.

Experimental Work:

Research into stiffened plates has been a subject of interest for many years. Due to the complexity of the problem and many parameters involved, extensive research efforts were devoted over the past years by many researchers to investigate varieties of aspects. Reinforcing the plate or the shell with the stiffener elements complicates the analysis, and several assumptions must be made in order to facilitate a solution. The complications increase if the stiffeners are not identical or unequally spaced. This situation might be beneficial for non uniform pattern of loadings, where larger stiffener sections or smaller spacing are more economical to use near the highly loaded regions. Inclination of the stiffeners might also be useful to improve the structural load carrying capacity. This, however, adds further complications to the analysis and modeling procedures.

In this paper, the height necessary to keep the plate within the limits of elasticity was (5 cm) and by using the limited elements procedure (LS. DYNA) program. AUTODYN (ANSYS, version 11), was specially designed for non-linear transient dynamic events such as ballistic impact, penetration and blast problems. The software is based on explicit finite difference, finite volume and finite element techniques which use both grid based and griddles numerical methods. A new material model, specifically designed for the shock response of anisotropic material has been implemented and couples of non-linear anisotropic constitutive relations with a Mie-Grüneisen equation of state. This program studies the status of the moving objects and tries to find out the outcome stresses. In most of the published research papers, most attention was given to study the high speeds of the objects and penetration status. But in this research, High light was shed on lower speeds as considering them the basic state in the engineering applications.
The case of the plate of entirely two fixed sides and free for the other two sides was studied. Five cases were studied ; the first of a plate without strengthener , the second state was with one medium content .The third was by using two terminal strengtheners .And the fourth case was by using two strengtheners 8 cm a part. The fifth was by u

 sing two strengtheners 4 cm apart .In all these cases, the strengtheners were 1 cm wide and 2 mm deep; to have them longitudinally used .i.e., the ends of the plates at the fixing points .The dimensions of the plate were 30 cm x 20 cm and 2 mm deep.

Results:

Experimentally: in the experimental work, the results of the deflection for all of the tests. Theoretically: all results of this part are shown in Figs. The results were also represented by Fig. After comparing the theoretical and the experimental work, a greatly- close results= were found. When using one strengthener , the maximum stress went down by(14 % ) and the maximum deflection by( 70% ) with comparison of without stiffener case .When using strengtheners at the ends, maximum stress was reduced to( 77%) and the deflection to (65%).When using strengtheners 8 cm a part , maximum stress went down by (56 % ) and the maximum deflection by ( 18%) . When using strengtheners 4 cm a part, maximum stresses went down by (60 %) and the maximum deflection by (31%). Conclusively, it is evident that it is better to use strengtheners at the ends or terminals, which is the best choice for such applications, because they reduce the stresses and deflection on the point of contact as possible. If reducing the stress and deflection of whole plate was preferred, the use of stiffeners at 4 cm a part is more suitable.
Fig. shows the relation between the stress and time which is calculated from the moment of contact. After that the stress is the rebound of the ball on plate.