Deterministyczne i stochastyczne sformułowanie perturbacyjne zagadnień układów belkowych ze szczelinami

The study concerns the beams with slots. The conditions of propagation of slots in bent beams are presented here, basing on the Griffith's proposed criterion of the released energy of distortion. There has been introduced a model of substitute joint of the section of slot affected beam, analysis of propagation of slot arrangement has been presented with the application of the adequate variation theorems. The spring issues as well as spring-plastic issues have been considered including the models of plastic zone in front of the top of the slot, as proposed by Irwin and Dugdale, quasi-static and dynamic questions have been discussed. A comparative analysis of the results based on the method proposed by this study has been conducted by use of finite element method (by means of commercial programmes MSC NASTRAN, ABAQUS, ANSYS) and the experimental research works. The substitute stiffness of the section of slot-affected beam has been determined by use of technical bending theory and cracking mechanics, the equivalence conditions of both models have been analysed. The experimental method has been proposed to determine this stiffness, verified for rectangular section steel beam. There is also presented perturbation stochastic formulation of own [specific] issue. All formulations have been conducted within systems with parameters defined both in the deterministic as well as the stochastic manner. In case of random systems a non-static methodology has been elaborated, basing on the linear analysis of the first two probabilistic moments of the values described in the perturbation form. The length and location of slots have been adopted as random variables. The results of the calculations such as the effect of the size and location of slots on the specific frequencies and forms, based on own programmes, have been presented in graphic form, in the two- and three-dimensional drawings.