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Báo cáo hóa học: " Research Article Positive Solutions for Some Beam Equation Boundary Value Problems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Positive Solutions for Some Beam Equation Boundary Value Problems | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 393259 9 pages doi 10.1155 2009 393259 Research Article Positive Solutions for Some Beam Equation Boundary Value Problems Jinhui Liu1 2 and Weiya Xu3 1 Department of Civil Engineering Hohai University Nanjing 210098 China 2 Zaozhuang Coal Mining Group Co. Ltd Jining 277605 China 3 Graduate School Hohai University Nanjing 210098 China Correspondence should be addressed to Jinhui Liu jinhuiliu88@163.com Received 2 September 2009 Accepted 1 November 2009 Recommended by Wenming Zou A new fixed point theorem in a cone is applied to obtain the existence of positive solutions of some fourth-order beam equation boundary value problems with dependence on the first-order derivative uiivft f t u t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 X 0 to X R 0 to is continuous. Copyright 2009 J. Liu and W. Xu. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction It is well known that beam is one of the basic structures in architecture. It is greatly used in the designing of bridge and construction. Recently scientists bring forward the theory of combined beams. That is to say we can bind up some stratified structure copings into one global combined beam with rock bolts. The deformations of an elastic beam in equilibrium state whose two ends are simply supported can be described by following equation of deflection curve 22 eioA iXi 1.1 x x where E is Yang s modulus constant Iz is moment of inertia with respect to z axes determined completely by the beam s shape cross-section. Specially Iz bh3 12 if the crosssection is a rectangle with a height of h and a width of b. Also q x is loading at x. If the 2 Boundary Value Problems loading of beam considered is in relation to deflection and rate of change of deflection we need to research the more