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Forming of the most convenient bent constructional elements with a permissible strength given

Fligiel M.

International Journal of Applied Mechanics and Engineering

2014

Vol. 19, no. 4

831--839

In the present study, the limiting values are determined of the criteria quantities of optimal forming of the most convenient bent supporting structure for the case of static loads in the range of the Hooke’s law applicability. As the criterion of the most convenient constructional element, the following were accepted: the smallest length of the activity of internal forces as well as the equal potential and the gradient of the potential energy of elastic deformation at each point of the constructional element.

Formation of the most optimal supporting construction in a two-dimensional state of load

Fligiel M.

International Journal of Applied Mechanics and Engineering

2012

Vol. 17, no. 3

799-810

In the present study, the most optimal supporting construction is sought. The notion of the most optimal support structure is defined. Two criteria are considered of an optimal formation of the most optimal support structure. The first criterion, i.e., the greatest rigidity of the structure, is fulfilled when the value of the unit potential strain energy over the entire volume of the structure is the same. The second criterion is known as the duration of the acting of forces of the supporting construction. The duration of the acting of forces is understood as the passage of internal forces along as short internal paths as possible. The seeking process of the most optimal supporting construction takes place in an iterative manner with a division of the structural space into finite elements. Seeking of the structural space is illustrated by two examples with the same mounting and stress conditions.