INVESTIGATION ON THE STRESS CONCENTRATION IN METALLIC FLAT PLATES DUE TO HOLES WITH DIFFERENT CONFIGURATIONS

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 7, July 2017, pp , Article ID: IJMET_08_07_189 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed INVESTIGATION ON THE STRESS CONCENTRATION IN METALLIC FLAT PLATES DUE TO HOLES WITH DIFFERENT CONFIGURATIONS Danish Handa Graduate Student, School of Mechanical Engineering, Lovely Professional University, Phagwara, Punjab, India. Raja Sekhar Dondapati Associate Professor, School of Mechanical Engineering, Lovely Professional University, Phagwara, Punjab, India Preeti Rao Usurumarti Assistant Professor, P. V. K. Institute of Technology, Anantpur, Andhra Pradesh, India. ABSTRACT Metallic Flat plates are used in various applications such as the wings of aircraft, locomotive shield, etc. These plates are subjected to holes for providing rivets or bolts. However, these holes would contribute to stress concentrations due to which the chances of failures would occur. Hence, in the present work, investigation of the effect of stress concentration factor in a flat plate with different geometrical configurations of a hole using a commercial finite element code ANSYS is performed. Further, analytical solutions are estimated for the stress concentration factor in a finite plate of a finite thickness having circular and elliptical holes in the Centre of the plate subjected to uniaxial tensile load. The obtained theoretical results were compared with numerical results and found to have a significant agreement. Key words: Circular Hole; Finite Element Method; Elliptical Hole; Stress Concentration Factor. Cite this Article: Danish Handa, Raja Sekhar Dondapati and Preeti Rao Usurumarti Investigation on The Stress Concentration in Metallic Flat Plates Due to Holes with Different Configurations. International Journal of Mechanical Engineering and Technology, 8(7), 2017, pp editor@iaeme.com

2 Investigation on The Stress Concentration in Metallic Flat Plates Due to Holes with Different Configurations 1. INTRODUCTION Here Researchers around the world are focusing attention on the development of stress-free metallic wings for aerospace applications. In the past, Kirsch derived a solution for the distribution of stresses over a central circular hole in an isotropic plate under uniform tensile stress. It was reported that Kirsch s solution showed a significant concentration of stresses at the boundary, by a factor of three when the applied stress was tensile in nature. Later, Inglis [1] during his work on a flat plate containing a central elliptical hole, derived the relation for stress concentration factor with respect to the applied stress by assuming the hole to be very far away from the plate boundary, that is an infinite plate. Further, considering two circular openings of identical dimensions, Dhir [2] determined the stress distribution around these openings in a thin large isotropic plate under biaxial normal stresses. No sooner Durelli et al [3] investigated stresses and strains around an elliptical hole in a long plate by analyzing a series of five plates with different widths. They used photo elasticity to determine the stresses and Moiré and Grids methods to determine strains. Furthermore, the distribution of stresses around the triangular holes with sharp corners in an infinite plate subjected to a tensile load was analyzed by Theocaris and Petrou [4]. Further, analytical functions for 2-D stress distributions around a triangular hole in a plate under the application of tensile load were developed by Daust and Hoa [5]. Length/height ratios of the triangular hole, the orientations of the load and the degree of the bluntness of the triangle vertex were taken into account in order to obtain the desired solutions. Further, using the complex potential method, Gao [6] obtained a general analytical solution for an elliptical hole in an infinite elastic plate subjected to biaxial loading conditions by employing the elliptic-hyperbolic coordinate system and assuming the hole boundary to be traction free. In addition, the characterization of thin walled cylindrical shells was derived by considering the similar loading conditions. A 3-D finite element analysis for evaluating the stress concentration factor in countersunk rivet holes in orthotropic laminated plates subjected to a uniaxial tensile load using ANSYS was conducted by Darwish et al [7]. Later, Enab[8] predicted the results of the stress concentration factor around the elliptical hole in unidirectional functionally graded material plates under uniaxial and biaxial loads by using ANSYS Parametric Design Language (APDL). Further, investigation of the distribution of stress around regular holes in a finite, isotropic and linearly elastic metallic plate by considering the uniaxial loading and assuming the plane stress conditions was performed by Jafari and Ardalani [9]. In the present scenario where the definite holes are necessary for the design of aircraft skin, leading to stress concentrations, researchers are focusing on the investigation of stress concentrations. Hence, in the present work, an investigation is performed to predict the stress concentrations in a metallic plate with different configurations of holes such as a circular and elliptical. In current times, computer simulations based on finite element analysis are being used due to the complexity involved in solving the mathematical equations. The next section explains the method of estimating stress concentrations in a flat plate with a hole using finite element method. 2. COMPUTATIONAL METHODOLOGY The methodology for the present work determines the equivalent Von Misses stresses in an isotropic flat plate with central circular and elliptical holes of different configurations by using a finite element code ANSYS. The following steps are carried out for conducting the finite element analysis: The model for analysis of the present study is defined as static editor@iaeme.com

3 Danish Handa, Raja Sekhar Dondapati and Preeti Rao Usurumarti Structural steel, an isotropic material is considered in the analysis of the present study. The mechanical properties for the same are Young s modulus (E) = 200GPa and Poison s ratio (ʋ) = 0.3. A rectangular plate of 100mm length (L), 50mm width (d) and 5mm thickness (t) with circular and elliptical holes of different dimensions are drawn in the center zone for the analysis. Realization of meshing process, the zones near discontinuities were refined. Further, define the load (1000N) along with direction and the boundary conditions that assures the static equilibrium. Perform analysis and obtain the results for Von Misses stresses. 3. EXPERIMENTAL RESULTS Since the current investigation is solely based on finite element model analysis and its consequences. Therefore, the validation of the results obtained from the finite element models is considered crucial. Hence, the values of stress concentration factor in a finite isotropic plate with a circular and elliptical in the center are obtained from the present finite element models for different dimensions of the hole and are compared with the results obtained from the literature reviewed Investigation of Stress Concentration Factor for A Flat Plate With A Central Circular Hole A finite isotropic flat plate with a central circular hole under uniaxial load has been considered as shown in Figure. Further, finite element models for the stress distribution around the circular holes of different diameters are shown in Fig. It can be seen from figure 3 that with the increase in the diameter, the stresses increase, therefore the stress concentration zone increases. Hence, the finite element results for the stress concentration factor with respect to the hole diameter are compared with the results obtained from Young and Budynas equation [10] and Heywood equation [11] as shown in Fig. Figure 1 Schematic model of the finite plate with a circular hole in the centre subjected to a uniaxial load editor@iaeme.com

4 Investigation on The Stress Concentration in Metallic Flat Plates Due to Holes with Different Configurations Figure 2 Variation of stress concentration factor with respect to the hole diameter of a central circular hole in a flat plate subjected to uniaxial load. Figure 3 Computational model of the finite plate with a circular hole in the centre subjected to a uniaxial load for different diameters of the hole editor@iaeme.com

5 Danish Handa, Raja Sekhar Dondapati and Preeti Rao Usurumarti 3.2. Investigation of Stress Concentration Factor for A Flat Plate With A Central Circular Hole Similar approach as in the previous section is performed for the analysis of the plate with an elliptical hole in the Centre. A finite isotropic flat plate with a central elliptical hole under uniaxial load has been considered as show in Fi.Further, finite element models for the stress distribution around the elliptical holes of different dimensions are shown in Figure. The finite element results for the stress concentration factor in a flat plate with elliptical holes of different dimensions are compared with the results obtained from the Young and Budynas equation [10] is shown in Fig. Figure 4 Schematic model of the finite plate with an elliptical hole in the centre subjected to a uniaxial load. Figure 5 Variation of stress concentration factor with respect to the major axis of a central elliptical hole in a flat plate subjected to uniaxial load editor@iaeme.com

6 Investigation on The Stress Concentration in Metallic Flat Plates Due to Holes with Different Configurations Figure 6 Computational model of the finite plate with an elliptical hole in the centre subjected to a uniaxial load for different dimensions of the hole. 4. DISSCUSSIONS The results of two cases: (1) A flat plate with a central circular hole; (2) A flat plate with a central elliptical hole, are obtained from the finite element analysis using a commercial code ANSYS. It is clearly illustrated by Fig and Fig that by keeping the width of the plate to be constant, the stress concentration factor directly varies with the hole geometry. Therefore, considering the same cross-section area and the load applied to the plate to be constant, the editor@iaeme.com

7 Danish Handa, Raja Sekhar Dondapati and Preeti Rao Usurumarti comparison of the finite element results of the stress concentration factor for circular and elliptical holes in a flat with respect to the cross-section area is determined in Fig. There is a large variation in the stress concentration factors for the elliptical hole when compared to thecircular hole. This may provide designers an efficient direction to estimate the effect of the hole on plate structures. Figure 7 Comparison of the stress concentration factor with respect to the area of cross-section for a thin finite isotropic plate with a central circular and elliptical hole. 5. CONCLUSION For designing engineering structures, the high stress concentration zone around a hole in a plate is of practical importance. Therefore a detailed finite element analysis was conducted for analyzing the effect of stress concentration factor around the central circular and elliptical holes in an isotropic flat plate subjected to a uniaxial tensile loading and determined that the stress concentration factor strongly depends on the dimensions of the holes. Some comparison analysis was performed to observe the accuracy of the results and found that the maximum overall error was less than 6%. In addition, results obtained from finite element analysis of circular and elliptical holes for the same configuration of the plate are compared and found that for the same cross-sectional area, there occurs a huge difference in the stress concentration factor. The results demonstrated here can be effective for designers to analyse the effect of stress concentrations under uniaxial loading conditions. However, for more complete and quantitative analysis of this problem, further study is necessary to understand the different parameters. REFERENCES [1] C. E. Inglis, Stresses in a plate due to the presnce of cracks and sharp corners, Trans. Inst. Naval Arch., vol. 55. pp , [2] S. K. DHIR, Stresses around two equal reinforced circular openings in a thin plate(stresses around two, Int. J. Solids Struct., vol. 4, [3] A. J. Durelli, V. J. Parks, and V. J. Lopardo, Stresses and finite strains around an elliptic hole in finite plates subjected to uniform load, Int. J. Non. Linear. Mech., vol. 5, no. 3, editor@iaeme.com

8 Investigation on The Stress Concentration in Metallic Flat Plates Due to Holes with Different Configurations [4] P. S. Theocaris and L. Petrou, Stress distributions and intensities at corners of equilateral triangular holes, Int. J. Fract., vol. 31, no. 4, pp , [5] Daust J.;Hoa S.V, An analytical solution for anisotropic plate containing triangular hole, Compos. Struct., vol. 19, pp , [6] X. L. Gao, A general solution of an infinite elastic plate with an elliptic hole under biaxial loading, Int. J. Press. Vessel. Pip., vol. 67, no. 1, pp , [7] F. Darwish, G. Tashtoush, and M. Gharaibeh, Stress concentration analysis for countersunk rivet holes in orthotropic plates, Eur. J. Mech. A/Solids, vol. 37, pp , [8] T. A. Enab, Stress concentration analysis in functionally graded plates with elliptic holes under biaxial loadings, Ain Shams Eng. J., vol. 5, no. 3, pp , [9] M. Jafari and E. Ardalani, Stress concentration in finite metallic plates with regular holes, Int. J. Mech. Sci., vol. 106, pp , [10] W. C. Young and R. G. Budynas, Roark s Formulas for Stress and Strain, vol. 7, no. 7th Edition [11] W. D. Pilkey and D. F. Pilkey, Peterson s Stress Concentration Factors, Third Edition [12] S. S. Deshpande, P. N. Desai, K. P. Pandey and N. P. Pangarkar, Consistent and Lumped Mass Matrices In Dynamics and Their Impact on Finite Element Analysis Results. International Journal of Mechanical Engineering and Technology, 7(2), 2016, pp editor@iaeme.com