Γενικό Τμήμα (Δημοσ. Π.Π. σε περιοδικά)

Permanent URI for this collection

Browse

Recent Submissions

Now showing 1 - 5 of 74
  • Thumbnail Image
    Item
    Open Access
    A note on the closed-form determination of zeros and poles of generalized analytic functions
    (Elsevier Science Publishing Co., Inc., 1989-12) Ioakimidis, Nikolaos
    The generalized method of Burniston and Siewert for the derivation of closed-form formulae for the zeros (and/or poles) of analytic functions inside a closed contour in the complex plane is further extended to the case of generalized analytic functions with real and imaginary parts satisfying homogeneous generalized Cauchy–Riemann equations. Two special cases and one generalization of this approach are also considered in brief.
  • Thumbnail Image
    Item
    Open Access
    The crack tip elastic stress field using computer algebra software
    (Pergamon Press, 1991) Ioakimidis, Nikolaos
    In various cases, we are interested in the equations for the elastic stress field components near a crack tip expressed in series forms. Frequently, the dominant terms in these series are not sufficient and additional terms are taken into account. Here we use the computer algebra system DERIVE in order to derive these series symbolically. (Additional popular computer algebra systems can also be successfully used.) The case of a finite straight crack under normal loading at infinity was selected for the illustration of the approach. The obtained symbolic results for the Westergaard complex potential, its derivative and the stress components are displayed in detail. The present results clearly show that the automatic symbolic series expansion of the components of the elastic field of interest near a crack tip is just a routine process if computer algebra software facilities are used.
  • Thumbnail Image
    Item
    Open Access
    Orders of singularity at wedge apices: the computer algebra approach
    (Pergamon Press, 1991) Ioakimidis, Nikolaos
    We illustrate the possibilities of computer algebra systems in performing the necessary tedious and, manually, error-prone symbolic computations during the determination of the orders of singularity at wedge apices in plane elasticity. The cases of the first, second and mixed fundamental problems for a simple wedge as well as the case of the first fundamental problem for a double wedge were used as examples of the approach (together with two special cases in crack problems). The rather elementary (yet powerful) computer algebra system DERIVE was used in the present formal computations.
  • Thumbnail Image
    Item
    Open Access
    Application of computer algebra to the iterative solution of singular integral equations
    (North-Holland (an imprint of Elsevier Science Publishers), 1992-01) Ioakimidis, Nikolaos
    The use of computer algebra systems in the approximate iterative solution of Cauchy-type singular integral equations (SIEs) appearing in crack problems of plane elasticity and in many additional branches of applied mechanics and engineering is proposed. The resulting method combining numerical and symbolic computations is called a SAN (semi-analytical/numerical) method. The computer algebra system DERIVE is used in the present computations, where the problem of a periodic array of collinear cracks has been selected for the illustration of the present approach. Extensive SAN results are displayed and their convergence is shown as well as their agreement (for the stress intensity factor) with the already available theoretical formula in this concrete application. Generalizations of the present SAN approach are completely possible.
  • Thumbnail Image
    Item
    Open Access
    Application of DERIVE to conformal mapping techniques in plane elasticity problems
    (Pergamon Press, 1991) Ioakimidis, Nikolaos
    Computer algebra systems have been already applied to several applied mechanics and plane elasticity problems. In this paper, we show the possibility of using DERIVE, a simple, but also powerful and modern computer algebra system, for the determination of the conformal mapping function in plane elasticity problems associated with holes (including triangles and squares). We display the obtained results in sufficient detail for the equilateral triangle and the square holes and we make several comments concerning the efficient use of DERIVE in the present application, where computer algebra systems seem not having been used up to now.