IRJET- Finite Element Analysis of a Laminated Conoid Shell under Uniform Pressure
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This document analyzes a four-layered rectangular laminated conoid shell with equal thickness layers in an anti-symmetrical stacking sequence. The shell is subjected to uniform pressure and analyzed using finite element analysis software ANSYS 15.0. The effects of varying the rise-to-span ratio from 0.05 to 0.5 on maximum principal stresses and deflection are studied. The results show that stresses increase with increasing rise-to-span ratio, with cross-ply laminates performing better than angle-ply. A rise-to-span ratio between 0.25-0.35 is found to provide better performance.
IRJET- Finite Element Analysis of a Laminated Conoid Shell under Uniform Pressure
- 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 07 Issue: 01 | Jan 2020 www.irjet.net p-ISSN: 2395-0072 © 2020, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 49 Finite Element Analysis of a Laminated Conoid Shell under Uniform Pressure Ram Ji Student of M.Tech in Structural Engineering and Construction Roorkee Institute of Technology, Roorkee (UTU) State Uttrakhand India ----------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - A four layered rectangular laminated Conoid shell in anti-symmetrical stacking sequence with equal thickness of layer for all sides clamped, all sides simply supported and two sides clamped two sides simply supported under transverse uniform pressure is analysed using ANSYS 15.0. The main objective is to study the effect of r/a ratio varying from 0.05 to 0.5 with an increment of 0.05 on the maximum principal stresses and deflection in structure under uniform pressure of magnitude 5000 kN/m2. Key Words: Static Analysis; Composites; Conoid; Cross-ply; Angle ply; Anti-symmetric; Rise-to-span Ratio; Orthotropic. 1. INTRODUCTION The stability of any structure is the main concern in any engineering construction.Materialswithhigherstrength to weight ratio are the most preferable to meet the desired requirements. Advancement in the modern technology Composite materials has been widely used now days for many purposes. Composites are light in weight compared to traditional materials Composites exhibit very high strength in all directions. There are many properties which make them the best suited material at present such as corrosion resistant, flexible in nature, easy and time saving in construction, low thermal conductivity, durable etc. 1.1 Shell and its Classification Shells are defined as the structures, which are essentially an expansion ofplainsurfacesorplatestobended plates and surfaces curved in geometry. Shells have small thickness in comparison to its other dimensions and have a curvature which differentiates it from plates. The shape of a shell structure spreads forces uniformly throughout the whole structure which means every part of the structure supports only a small part of the load which provides strength to the structure. Membrane action in shells is primarily due to the plane stresses whereas the secondary forces also occur due to the flexural deformations. Fig - Classification of shells 1.2 Conoid Shell and its Applications These are the doubly curved shells which are anticlastic in nature. They have negative Gauss curvature and membrane governing equation of the conoid shells is hyperbolic. These are the ruled surfaces with one edge curved and other edge straight. A conoid is ruled surface, whose rulings (lines) follow these conditions: 1. All rulings are parallel to plane –the directrix plane. 2. All rulings intersect a fixed line - the axis. 2. FEM and its Importance FEM is a numerically based approach which is utilized in solving many engineering problems such as structural analysis, heat transfer, fluid flow, mass transport and electromagnetic potential. There are basically three types of finite elements: 1. One-dimensional element 2. Two-dimensional element 3. Three-dimensional element 2.1 Clamped Conoid with CP laminate The maximum stresses and maximum deflection with increasing rise are given in Table and discussed below
- 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 07 Issue: 01 | Jan 2020 www.irjet.net p-ISSN: 2395-0072 © 2020, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 50 RS R 1st princi pal stress σ1 (kN/ m2) 2nd princi pal Stress σ2 (kN/ m2) 3rd princi pal Stress σ3 (kN/ m2) Shear stress τxy (kN/ m2) Shear Stress τyz (kN/ m2) Shear Stress τxz (kN/ m2) Deflect ion UZ(m) 0.0 5 .178E+ 08 75295 9 1713.5 5 47136 7 85790 8 .121E +07 .75375 3 0.1 .123E+ 08 46084 0 4414.7 33912 0 81953 2 .107E +07 .31530 1 0.1 5 .891E+ 07 41288 3 7720.5 30735 8 86505 0 .117E +07 .20440 5 0.2 .795E+ 07 35160 5 11698. 7 27909 3 84670 8 .130E +07 .14171 3 0.2 5 .651E+ 07 22660 4 12758. 5 49580 6 46743 4 .224E +07 .10309 4 0.3 .752E+ 07 35093 7 91487. 9 66162 9 84578 8 .361E +07 .19468 4 0.3 5 .835E+ 07 42047 0 10032 9 72787 5 .114E +07 .353E +07 .23336 8 0.4 .916E+ 07 48800 7 10369 8 72987 0 .144E +07 .343E +07 .27665 7 0.4 5 .993E+ 07 57259 6 11089 0 73109 6 .179E +07 .345E +07 .32392 5 0.5 .106E+ 08 74166 8 11057 4 74897 5 .208E +07 .347E +07 .37243 5 Maximum transverse shear stress (τyz) and (τxz) The variation of maximum shearstresseswith respectto rise to span ratio (r/a) is presented in figure 4.7 graphically. Stresses increase with increase in rise tospanratio.Increase in stresses in yz and xz is large as compared to decrease in stresses in shear stress xy. Maximum stress in shear in yz and xz direction is 0.208*107 kN/m2at RSR 0.5 and 0.361*107kN/m2 at RSR 0.3 respectively. Chart -1: Maximum shear stress (τxy, τyz and τxz) for CCCCCP laminate 3. CONCLUSIONS In the present report, conoid shell with changingrisetospan ratio along with various boundary conditions is analyzedfor principal stresses and deflections under uniform transverse pressure by using finite element method. a) Cross ply performs better than angle ply laminates. b) Boundary condition all sides clamped (CCCC)cross ply found to give better results than all other cases. c) Rise to span ratio of 0.25-0.35is found suitable for better performance of the Conoid shell. ACKNOWLEDGEMENT It gives me a great pleasure and satisfaction to present the Research Paper entitled “Finite Element Analysis of a Laminated Conoid Shell under Uniform Pressure”. The success of my Research paper depends largely on the encouragement and guidelines of my guide Miss Swati Dhiman. REFERENCES Daryl L. Logan, “A First Course in the Finite Element Method”, Nelson a divison of Thomson Canada Limited, Fourth edition, 2007. Daniel Ishai “Engineering Mechanics of Composite Material”, Oxford University press, Second edition, 2006. IS: 2210:1988; “Criteria for design of reinforced concrete shell structures and folded plates”. Sahoo, Sand Chakravorty, D,“Finite Element vibration characteristics of composite hyper shallow shells with various Edge supports”, Journal of vibration and control, Vol 11, Pp 1291-1309, 2005. BIOGRAPHIES Author of this Research Paper is Pursuing M.tech in Structural Engineering and Construction at RIT Roorkee. He is completed B.Tech in Civil Engineering and Polytechnic in ECE.