The Selection Of The Stress Function When The Rectangular Section Beam Subjected To Arbitary Polynomial Distributed Load

At the late of the17th, the principleof the rectangular section beam had already beenstudied. So far, we has achieved a major breakthrough and it has a wide range ofapplication prospects in housing construction, industrial equipment, roads, bridges and soon.Stress function is an important tool to solve the plane problem in mechanics ofelasticity. In other words, the stress solution for the plane problem in mechanics ofelasticity is to solve the biharmonic equation which satisfies all the boundary conditions. Itis wery difficult and unnecessary to solve the biharmonic equation in terms of the puremathematics. So, the inverse methord is often used to make a stress function which meetsboth the biharmonic equations and boundary conditions in elasticitic mechanic. This paperis mainly devoted to study the section of the stress function when the rectangular sectionbeam is subjected to arbitrary polynomial distributed load.Firstly, with regard to the rectangular section beam subjected to any quarticpolynomial distributed load, a uniform stress function which meets both the biharmonicequations and boundary conditions is constructed based on the theory of elastic mechanicsby using the inverse method to select several exponential polynomial or an individualitems of different exponential polynomial. Thus, the stress components are solved.Furthermore, the article carried on the theoretical derivation in allusion to the rectangularsection beam in engineering components, such as steel structure. the experimental resultswhich is tested by static strain tester are in accord with the theoretic calculation, it meansthat the results are accurate. Therefore, the solution paves the way for the analysis andsolution of the rectangular section beam.Secondly, in view of the rectangular section beam under higher polynomial, namelyquintic polynomial distributed load, a detailed research is conducted on the basis of thefront, also a new stress function is also constructed, the stress components are solved and aengineering example is given.Finally, in terms of the rectangular section beam subjected to any polynomial distributed load, a uniform stress function which meets both the biharmonic equations andboundary conditions is constructed and a more general regularity of mechanics ofelasticity is summed up. What is more, it verified the correctness of the former results. It isof great theoretical and practical significance.