Nelineární úlohy nosníků na pružném podkladu

Abstract

This dissertation thesis deals firstly with the solution of the linear problems of bending the support placed on an elastic foundation by means of deterministic and probability approaches - method SBRA (Simulation – Based Reliability Assesment). The thesis also deals with the solution of bending the support placed on a nonlinear elastic foundation using the finite difference method and the Newton method. The results for linear approximations and the different degrees of polynomial and other nonlinear approximations are compared here. Another major part of the thesis deals with the investigation of the possibility of using an elastic foundation in the tangential direction, where the support surrounded by the semi-space is subjected to axial pulling. The aim of the thesis is to determine suitable dependencies (the author’s own new model designs, analysis, theory and solution, design of physical models of the base behaviour) by analytical approach, numerical solution using the finite element method and experimental measurement. Various cases of the elastic foundation in the tangential direction are solved by analytical approach and the method of central differences. The thesis also deals with exploration of possible stiffness approximations, leading to the calculation of the coefficient of compressibility of the foundation. Verification of the proposed models is compared to the results of the numerical method. Experimental testing of the proposed tangential elastic foundation models is performed by pull-out tests. For the experimental measurement, a practice example is used, namely pulling bone screws from the bones (the femoral neck fracture) – biomechanics. Pull-out tests are especially important for research on the behaviour of implants in medicine. For experimental measurement, the author’s own product for mounting screws in the TESTOMETRIC machine has been designed and made. Moreover, the bone screws have been slightly adapted to the needs of the experiment. In the first phase of testing, however, the bone bolts (screws) are pulled from a wooden sample (dry spruce), and in the next phase from a bovine bone cadaver (biomechanics). The data obtained from the experiments is then evaluated and compared.