Engineering Transactions,
8, 3, pp. 603-625, 1960
Niektóre Zagadnienia Wytrzymałości Tarczy Nieograniczonej z Ośrodkiem Sztywnym
The problem of an infinite plate with a rigid inclusion is solved by conformal mapping of the rigid inclusion into the unit circle. This problem has been solved by G.N. SAVIN, [3], by different methods. In this paper the method of F. SZELĄGOWSKI is used, the principal stress being laid on the obtainment of numerical data for steel.
One-directional tension of an infinite plate is considered and the case where the rigid inclusion is cooled down from a higher temperature to a lower temperature. Equations for the state of stress in the plate are derived for an inclusion in the form of a generalized ellipse (circle, ellipse proper, rectilinear slit), a triangle and a curvilinear square. The problem of a plate with a rigid inclusion in the form of a curvilinear square is considered for various positions in relation to the direction of tension. All the above forms of the rigid inclusion may be mapped conformally by means of one mapping function. This function is characterized by two coefficients deciding upon the shape of the rigid inclusion. This facilitates the analysis of the influence of the form of the inclusion on the state of stress in the plate. Besides of the general solution, closed formulae are determined for stresses at some characteristic points of rigid inclusion. the infinite plate with various shapes of the Numerical values of these stresses are determined for a steel plate. The results of analysis are important chiefly for steel bridge structures. For, they enable to determine the influence on stress concentration of the form of the elements welded to the plate. The theoretical part of the present paper constitutes in a certain sense a generalization of Ref. [2].
One-directional tension of an infinite plate is considered and the case where the rigid inclusion is cooled down from a higher temperature to a lower temperature. Equations for the state of stress in the plate are derived for an inclusion in the form of a generalized ellipse (circle, ellipse proper, rectilinear slit), a triangle and a curvilinear square. The problem of a plate with a rigid inclusion in the form of a curvilinear square is considered for various positions in relation to the direction of tension. All the above forms of the rigid inclusion may be mapped conformally by means of one mapping function. This function is characterized by two coefficients deciding upon the shape of the rigid inclusion. This facilitates the analysis of the influence of the form of the inclusion on the state of stress in the plate. Besides of the general solution, closed formulae are determined for stresses at some characteristic points of rigid inclusion. the infinite plate with various shapes of the Numerical values of these stresses are determined for a steel plate. The results of analysis are important chiefly for steel bridge structures. For, they enable to determine the influence on stress concentration of the form of the elements welded to the plate. The theoretical part of the present paper constitutes in a certain sense a generalization of Ref. [2].
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References
F. SZELĄGOWSKI, Rozwiązanie zagadnienia płaskiego teorii sprężystości w układzie współrzędnych prostokątnych, Rozpr, inzyn., 1, 1 (1953).
F., SZELĄGOWSKI, O pewnych szczególnych przypadkach wytrzymałości tarczy nieograniczonej z odmiennym ośrodkiem zarysu eliptycznego, Rozpr. inzyn., 1, 1 (1953).
[in Russian]