Upper Saddle River Boston Columbus San Francisco New York Indianapolis London Toronto Sydney Singapore Tokyo Montreal Dubai Madrid Hong Kong Mexico City Munich Paris Amsterdam Cape Town Introduction to Finite Elements in Engineering FOURTH EDITION TIRUPATHI R. CHANDRUPATLA Rowan University Glassboro, New Jersey ASHOK D. BELEGUNDU The Pennsylvania State University University Park, Pennsylvania ©2012 Pearson Education, Inc. Upper Saddle River, NJ. All Rights Reserved.