Some new contributions related to structural problems in engineering

Abstract

<p>The studies in this PhD thesis are focused on some problems of general interest in applied mathematics and engineering sciences. A very broad view is used from contributions which can be directly used for solving some important structural problems in engineering sciences, to contributions which also are of interest in pure mathematics. The main body of the PhD thesis consists of five papers (papers A - E). <p>In Paper A a new presentation of the mathematical theory of linear elasticity from a functional analytic standpoint is given. Moreover, a useful estimate of the Sobolev norm in <i>R ⁿ</i> is given. Finally, the problem connected to non-linear beams on elastic foundation is modelled and analyzed. <p>In Paper B we present a new method to evaluate the sliding stability of flat slab buttress dams. Moreover, we investigate the possibility of utilizing safety capacity in neighbouring pillars within a section to show that the entire section has adequate capacity against sliding in the dam-foundation interface. <p>In Paper C we present some new thoughts on and a discussion of an overview of different numerical methods that may be applied to evaluate the stability of dam structures. In particular, in this light we discuss and compare with 14 different case studies from the literature where numerical methods have been used to study the behaviour of gravity and plate dams. Finally, we identify and discuss advantages and disadvantages of different methods of modeling failure modes. <p>In Paper D we prove and discuss some new Fourier inequalities in the general frame of Lorentz-Zygmund spaces and in the case with unbounded orthogonal systems. The derived results generalize, complement and unify several results in the literature for this general case. <p>In Paper E we consider some mathematical aspects of the torsion problem for anisotropic periodic plate-structures where the underlying material is monoclinic. In particular, we show in detail how the weak formulation of the problem is derived and express the torsional rigidity in terms of its solution. <p>These new results are put into a more general frame in an Introduction, where, in particular, a comparison with some new international research and broad view of such interplay between applied mathematics and engineering problems is presented and discussed.