TABLE OF CONTENTS Table of Contents PARAMETRIC STUDY OF SANDWICH PANEL BUCKLING IN COMPOSITE WIND TURBINE BLADES Shicong Miao, Steven Donaldson, Elias Toubia……………………………………………………………………….….……3 A STUDY OF SIMPLIFIED SHALLOW WATER WAVES: ASSESSMENT OF ADOMIAN’S DECOMPOSITION METHOD FOR THE ANALYTICAL SOLUTION Mehdi Safari……………………………………………………………………………………….……………………..….…….16 ON BICRITERIA LARGE SCALE TRANSSHIPMENT PROBLEMS Dr. Jasem M.S. Alrajhi, Dr. Hilal A. Abdelwali, Dr. Mohsen S. Alardhi, Eng. Rafik El Shiaty…….…………..…..….21 TRIBOLOGY OF HIGH SPEED MOVING MECHANICAL SYSTEMS FOR SPACECRAFTS - TRIBOLOGICAL ISSUES K. Sathyan……………………………………………………………………………………………………..…………..……....27 THE USE OF IRON IN PEAT WATER FOR FENTON PROCESS Mirna Apriani, Ali Masduqi……………………………………………………………………………………..……….……..35 TRIBOLOGY OF HIGH-SPEED MOVING MECHANICAL SYSTEMS FOR SPACECRAFTS: LUBRICATION SYSTEMS OF BALL BEARINGS K. Sathyan………………………………………………………………………………………………………………………..39 <strong>Academy</strong><strong>Publish</strong>.org – Journal of Eng<strong>in</strong>eer<strong>in</strong>g and Technology Vol.2, No.2 2
PARAMETRIC STUDY OF SANDWICH PANEL BUCKLING IN COMPOSITE WIND TURBINE BLADES Shicong Miao, Steven Donaldson, and Elias Toubia Parametric Study of Sandwich Panel Buckl<strong>in</strong>g <strong>in</strong> Composite W<strong>in</strong>d Turb<strong>in</strong>e Blades Shicong Miao, Steven Donaldson * , and Elias Toubia *Correspond<strong>in</strong>g author: steven.donaldson@notes.udayton.edu Department of Civil and Environmental Eng<strong>in</strong>eer<strong>in</strong>g, University of Dayton, Dayton, OH 45469. USA ABSTRACT: A parametric study of the buckl<strong>in</strong>g per<strong>form</strong>ance of composite w<strong>in</strong>d turb<strong>in</strong>e blade regions with th<strong>in</strong> symmetric lam<strong>in</strong>ated sandwich rectangular panels, subjected to uni<strong>form</strong> axial shell edge compression loads is presented. The research focused on the critical buckl<strong>in</strong>g load and stra<strong>in</strong> levels with core material parameters, such as transverse core shear modulus and core thickness, for rectangular sandwich strips with long aspect ratios. Both flat and curved-section models were considered. The buckl<strong>in</strong>g design plots generated provide an <strong>in</strong>sight <strong>in</strong>to optimal core solutions for efficient designs. NOMENCLATURE a = length of the panel, m b = width of the panel, m c = core thickness, m k = panel curvature ratio, % (arc height divided by the panel width) l = curve length, m r = radius, m t = fac<strong>in</strong>g thickness on one surface, m h = overall thickness of sandwich C 0 = normalized core thickness (core thickness divided by total fac<strong>in</strong>g sheet thickness) 1, 2, 3 = general coord<strong>in</strong>ates. (1:longitud<strong>in</strong>al direction; 2: width direction; 3: direction normal to the panel plan<strong>form</strong>) r, t, z = cyl<strong>in</strong>drical coord<strong>in</strong>ates. (r: radial direction normal to panel; t: curve angle direction; z: longitud<strong>in</strong>al direction) U 1, U 2 , U 3 = displacement <strong>in</strong> 1, 2, 3 direction U r, U z , U t = displacement <strong>in</strong> r, z, t direction P cr = critical buckl<strong>in</strong>g end load (=eigenvalue), N/m ε cr = critical buckl<strong>in</strong>g end stra<strong>in</strong>, % E 1 , E 2 , E 3 = Moduli of elasticity G 13 = Core transverse shear modulus <strong>in</strong> 1-3 plane, Pa G 23 = Core transverse shear modulus <strong>in</strong> 2-3 plane, Pa ν 12 , ν 21, ν 23 = Poisson's ratios N 1 = Uni<strong>form</strong> compressive end load, N/m INTRODUCTION Renewable energy sources cont<strong>in</strong>ue to <strong>in</strong>crease as a percentage of global energy production. This trend is dom<strong>in</strong>ated by w<strong>in</strong>d energy and is the result of both an <strong>in</strong>crease <strong>in</strong> the number of turb<strong>in</strong>es <strong>in</strong>stalled, as well as the <strong>in</strong>creas<strong>in</strong>g diameter of turb<strong>in</strong>e rotors with the correspond<strong>in</strong>g energy output per turb<strong>in</strong>e (Roczek, 2010). As a consequence of this design strategy, the blade structures are becom<strong>in</strong>g <strong>in</strong>creas<strong>in</strong>gly th<strong>in</strong>walled, such that buckl<strong>in</strong>g problems <strong>in</strong> the blade panels must be addressed (Lund, Johansen, 2008). In general, the w<strong>in</strong>d turb<strong>in</strong>e blade works <strong>in</strong> much the same way as the steel I-beam, except that there are shells around the outside that <strong>form</strong> the aerodynamic shape and resist buckl<strong>in</strong>g and torsional loads (WE Handbook- 3- Structural Design). Utility-scale w<strong>in</strong>d turb<strong>in</strong>e blades use extensive sandwich construction, <strong>in</strong> both the aerodynamic shells and shear webs. To meet stiffness constra<strong>in</strong>ts such as deflection limits, the fiber composite materials <strong>in</strong> the broad unsupported spans of shell and shear web lam<strong>in</strong>ates are stiffened through the use of sandwich construction to prevent local de<strong>form</strong>ation and buckl<strong>in</strong>g. In blade structures, the largest s<strong>in</strong>gle role of the sandwich core is to assure adequate stability of the large panel regions aga<strong>in</strong>st buckl<strong>in</strong>g. As such, the most significant attributes of the core materials are the transverse shear modulus and the core thickness. S<strong>in</strong>ce core materials are generally available <strong>in</strong> a wide range of weights, mechanical properties, and cost, a study focused on the shell core is appropriate. Several related and valuable plate buckl<strong>in</strong>g studies and w<strong>in</strong>d turb<strong>in</strong>e blade prelim<strong>in</strong>ary design studied have been done <strong>in</strong> this area. General w<strong>in</strong>d turb<strong>in</strong>e blade optimization methods are discussed and presented <strong>in</strong> (Roczek, 2010, Lund, Johansen, 2008 and Lund, 2005). Structural reliability and mechanical behavior predictions for blade materials are reported <strong>in</strong> reference (Mishnaevsky et al., 2011). A prelim<strong>in</strong>ary design study of an advanced 50 m blade for utility w<strong>in</strong>d turb<strong>in</strong>es is presented <strong>in</strong> reference (Jackson et al., 2005) Closed <strong>form</strong>, exact solutions for the buckl<strong>in</strong>g of simply supported, rectangular, orthotropic plates under different load conditions are given <strong>in</strong> (Narita, Leissa, 1990, Leissa, 1985). Many nondimensional buckl<strong>in</strong>g parameters were generated by Nemeth and Weaver ( Nemeth, 1995, Nemeth 2004, Weaver, Nemeth, 2007) for long or <strong>in</strong>f<strong>in</strong>itely long symmetrically lam<strong>in</strong>ated anisotropic rectangular plates subjected to various comb<strong>in</strong>ed load conditions. Theoretical prediction of buckl<strong>in</strong>g loads for cyclic sandwich shells under axial compression with lam<strong>in</strong>ated fac<strong>in</strong>gs and foam core is presented <strong>in</strong> (Morovvati, 2011). Although many researchers have <strong>in</strong>vestigated the buckl<strong>in</strong>g of simply supported lam<strong>in</strong>ated composite plates, the early buckl<strong>in</strong>g analysis works focused on anisotropic plate <strong>Academy</strong><strong>Publish</strong>.org – Journal of Eng<strong>in</strong>eer<strong>in</strong>g and Technology Vol.2, No.2 3