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  • 1.
    Atashipour, Seyed Rasoul
    et al.
    Luleå University of Technology, Department of Civil, Environmental and Natural Resources Engineering, Structural and Construction Engineering.
    Girhammar, Ulf Arne
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Wood Science and Engineering.
    On the Shear Buckling of Clamped Narrow Rectangular Orthotropic Plates2015In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, Vol. 2015, article id 569356Article in journal (Refereed)
    Abstract [en]

    This paper deals with stability analysis of clamped rectangular orthotropic thin plates subjected to uniformly distributed shear load around the edges. Due to the nature of this problem, it is impossible to present mathematically exact analytical solution for the governing differential equations. Consequently, all existing studies in the literature have been performed by means of different numerical approaches. Here, a closed-form approach is presented for simple and fast prediction of the critical buckling load of clamped narrow rectangular orthotropic thin plates. Next, a practical modification factor is proposed to extend the validity of the obtained results for a wide range of plate aspect ratios. To demonstrate the efficiency and reliability of the proposed closed-form formulas, an accurate computational code is developed based on the classical plate theory (CPT) by means of differential quadrature method (DQM) for comparison purposes. Moreover, several finite element (FE) simulations are performed via ANSYS software. It is shown that simplicity, high accuracy, and rapid prediction of the critical load for different values of the plate aspect ratio and for a wide range of effective geometric and mechanical parameters are the main advantages of the proposed closed-form formulas over other existing studies in the literature for the same problem.

  • 2.
    Fakharian, Ahmad
    Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Signals and Systems.
    Design of switching multiobjective controller: A new approach2011In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, Vol. 2011Article in journal (Refereed)
    Abstract [en]

    Design of switching H 2 / H ∞ output-feedback controller for discrete-time LTI systems with state-multiplicative noise is considered. The closed loop system achieves a minimum bound on the stochastic H 2 performance level, while satisfying the H ∞ performance. The proposed controller is based on a fuzzy supervisor which manages the combination of two separate H 2 and H ∞ controllers. A convex formulation of the two controllers leads to a structure which benefits from the advantages of both controllers to ensure a good performance in both the transient phase (H 2 controller) and the steady phase (H ∞ controller). The stability analysis uses the Lyapunov technique, inspired from switching system theory, to prove that the closed loop system with the proposed controller structure remains globally stable despite the configuration changing

  • 3.
    Lukkassen, Dag
    et al.
    Narvik University College and Norut Narvik.
    Meidell, Annette
    Narvik University College, 8505 Narvik, Norway.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    A new approach for estimating the friction in thin film lubrication2010In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, Vol. 2010Article in journal (Refereed)
    Abstract [en]

    An important problem in the theory of lubrication is to model and analyze the effect of surface roughness on, for example, the friction and load carrying capacity. A direct numerical computation is often impossible since an extremely fine mesh is required to resolve the surface roughness. This suggests that one applies some averaging technique. The branch in mathematics which deals with this type of questions is known as homogenization. In this paper we present a completely new method for computing the friction. The main idea is that we study the variational problem corresponding to the Reynolds equation. We prove that the homogenized variational problem is closely related to the homogenized friction. Finally we use bounds on the homogenized Lagrangian to derive bounds for the friction. That these bounds can be used to efficiently compute the friction is demonstrated in a typical example

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