Some new solutions on large deflections of beams

Large deflections which become under various loading on bearer systems are well known and there are many researches on this subject. Since this subject is very important, related studies are going on currently. The obtained results by linearization can be sufficient in many cases of the engineering fields. However, the well known curvature relation of elastic curve is not linear and as that of real material?s stress-strain relation. Taking this fact into consideration, large deflections cannot be analyzed by analytic methods all the times. When this is the case, approximate and numerical methods should be used. In this thesis, weighted residual and Runge-Kutta methods are mostly used. Both material and geometrical nonlinearity are investigated jointly in most of the sections of the thesis. The introduction part of the thesis includes the state of the art, the aim of this research and the contribution to literature. In section 2, Firstly, the relation of stress-strain of beam material is assumed as Ludwick type and then large deflections of cantilever beam which is subjected to moment at the free end are calculated. Then the same process is applied to the type of cubical and logarithmic stressstrain relations. In section 3, the large deflections of the cantilever beam which is subjected to concentrated load at the free end are calculated using different methods and finally, the compared results are presented. In sections 4 and 5, the large deflections of the uniform distributed loaded simple beams and combined loaded cantilever beams are calculated by numerical methods using curvaturemoment equations which are obtained by assuming different arc lengths. In sections 6 and 7, composite beams are investigated. In section 6, composite cantilever beams which is subjected to concentrated load for only geometrical non-linearity is considered. In section 7, for both non-linearity, the large deflections of the composite cantilever beams which is subjected to moment at the free end are calculated for Ludwick, cubical, and logarithmic types of stress-strain relations. In section 8, the large deflections of the non-linear bimodulus cantilever beam which is subjected to moment at the free end are investigated for cubical and logarithmic materials. Afterward, the large deflections of the linear bimodulus cantilever beam which is subjected to concentrated load at the free end or subjected to combined load are calculated by assuming different arc length. The same process is applied to uniform distributed loaded linear bimodulus simple beams and obtained results for each cases are presented in the tables. In this thesis, simple and understandable solutions have been proposed instead of known complex solutions from the previous studies in this area. Also, some new solutions have been presented for less encountered composite and bimodulus beams. Keywords: Large deflections, material nonlinearity, geometrical nonlinearity, composite beams, bimodulus beams.