Method for determining the location of additional supports of a simply supported Kirchhoff plate under random action

Аuthors

Borshevetskiy S. A.

PJSC Yakovlev , 68, Leningradskiy prospect, Moscow, 125315, Russia

e-mail: wrdeww@bk.ru

Abstract

An integral trend in modern mechanical engineering is to increase the efficiency of manufactured products. In aircraft such as airplanes, this could be achieve by reducing the weight of the structure, which is achieved through the using of skins and panels, which are thin shells that are not capable of independently carrying any small load. Therefore, to increase rigidity, they are additionally fixed. The analytical approach to problems with large plates or shells with a large number of additional supports has many difficulties due to the size of the resulting system.

The main objective of the new proposed method is to obtain analytical relationships between the type of external load and the location of additional supports based on the conditions of structural rigidity. The problem solving in several stages and uses well-known mathematical methods.

The first step is to determine the maximum size of a single segment of the structure that satisfies the required stiffness condition. For universality, the problem is solved using the influence function (Green's) and the system's response to a unit load is obtained in the form of the Dirac delta function.

The second stage is to determine the location of only four (and in a non-stationary setting, only two) additional supports. The solution is the maximum value of the radius of the location of the fastenings that satisfy the condition of structural rigidity.

At the third stage, the required number and location coordinates of additional supports calculating for the entire structure as a whole, with possible adjustments to the sizes of the resulting segments.

The last stage can be numerical verification using modern modeling and calculation methods.

The undoubted advantage of the proposed method is its analytical form of solving the problem, which allows the method to using for various geometric and physical characteristics of the plates, as well as to apply an arbitrary load to any place. In general, the technique could be extend to curved shells. This will require the transition of the equation of motion of the structure to the local coordinate system of the shell, which will subsequently allow the shell to be “unfolded” into a rectangular plate. At the same time, the analytical form of solving the problem, as well as the essence of the technique and its advantages, are completely preserved.

Keywords:

Kirchhoff plate, structural rigidity, random load, structural rigidity, pivotally supported plate, influence function

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