Οριακή ανάλυση και ανάλυση προσαρμογής κελυφωτών μεταλλικών κατασκευών υπό το κριτήριο διαρροής Ilyushin

Abstract

In engineering practice structures are often subject to variable or cycling loading. While the actual load history of the loading is unknown, the loads are usually bounded inside a load domain. The behavior of a structure subject to variable loads can be classified by one of the following cases: 1. If the loads remain at sufficiently low levels, structure’s response is purely elastic. 2. However if the applied loading is sufficiently high, the structure exceeds its load-carrying capacity and eventually it reaches the point of plastic collapse. 3. If the plastic strain increments does not change sigh with each load cycle, after a number of cycles, the total strains and displacements grow large enough to ultimately cast the structure unserviceable due to excessive plastic deformation accumulation. This steady state response is called incremental plasticity or ratcheting. 4. On the other hand if the plastic strain increments do alternate sign with each load cycle, they tend to cancel each other and while the total structure deformation remains small, in the points of intense stress local material failures develop, after a sufficient number of cycles. This failure mode is called alternating plasticity or low-cycle fatigue. 5. After some time plastic deformations cease to develop further and the accumulated dissipated energy remains bounded. Response of the structure is purely elastic after the initial transient response, where plastic deformation appears during the initial cycles. This phenomenon is called adaptation or elastic shakedown. The essence of shakedown analysis is to determine how much we can expand or contrast a load domain of variable loads so to be certain that the elastoplastic structure subject to these loads will shakedown. Applications of shakedown analysis include, but are not limited to, pipe junctions, storage tanks and silos, pressure vessels, nuclear reactors, road pavements and train rails. The goals of this thesis are summarized to the following: - To make use of the classic elastoplastic material model and the Ilyushin yield criterion in the computational realization of shakedown analysis of metal structures. - To use - if possible – proved reference mathematical programming software and algorithms. - To develop computer programs capable of analyzing shell structures under the Ilyushin criterion utilizing the finite elements method and produce the necessary input dad for feeding the mathematical programming software. - To perform numerical applications on model structures of practical value from the engineering point of view and to evaluate the performance of the suggested formulation. The body of the dissertation comprises eight chapters. In the first introductory chapter a short mention of the adaptation phenomenon and its application along with a review of state of the art is written. Also the motives and aims of this thesis are outlined. The second chapter introduces elements of the finite elements method (FEM) concerning shells and especially the various options for modeling shell structures. Also there is reference on the non-orthogonal coordinates system, in order to gain a full picture of the shell element that was chosen for the modeling of the structures of the numerical applications. In the third chapter we have the full description of the Morley shell element, also known as the constant stress resultant shell element, which is the one we used to model the structures of the numerical applications of this thesis.