IN MECHANICS OF DEFORMABLE SOLIDS PRIMARY PLASTIC ON PANEL DURING POWER UP DEVELOPMENT OF DEFORMATIONS
DOI:
https://doi.org/10.61413/CIPR3225Keywords:
deformation, panel, plate, composite material, concentrationAbstract
One of the most important issues in solid mechanics is the development and application of optimal methods for estimating the resistance of dispersion materials. Currently, the theory of propagation of cracks in solid bodies is widespread due to the wide use of high-strength materials and large-sized structures and devices in various fields of technology.
The article discusses the methods of studying the problems of the interaction of two factors - strengthening the panel with stiffening ribs made of unidirectional composite material and weakening it with a number of circular holes and cracks protruding from its contour.
An infinite isotropic elastic riveted panel weakened by a periodic system of circular holes and two cracks along the abscissa axis segments near each hole is considered. The contours of the holes and the edges of the cracks are free from external forces. Transverse stiffness ribs made of metal composite material are riveted to the plate. In the calculation scheme, the effect of riveted reinforcing ribs is replaced by the concentrated forces applied at the points of location of the rivets. The values of the concentrated forces are found depending on the geometrical and physical parameters of the problem. Stress intensity factors and ultimate loadings were calculated depending on the geometrical and physical parameters of the problem. It has been shown that there is a stable phase of crack development under certain specified conditions.
The development of initial plastic deformations (embryonic cracks) emerging from the contour of circular holes in a plate reinforced with stiffness ribs is studied. The material of the plate is elastic-perfect-plastic satisfying the Tresca-Saint-Venant condition. It is assumed that the plastic deformations are concentrated along some slip lines emanating from the contour of the hole. By satisfying the boundary conditions, the solution of the problem leads to a singular integral equation. Then the singular equation of the problem is brought to a system of algebraic equations without the intermediate step of bringing it to the Fredholm equation. The resulting system was solved by the Gaussian method with the selection of principal elements for different values of n (n is the number of Chebyshev nodes in the division of the interval). The values of concentrated forces are found depending on the geometrical and physical parameters of the problem. The dependences of the length of the plasticity bands on the applied load, the geometrical parameters of the problem and the yield point of the material were found.
Using the local dissipation condition (KPT-criteria), a ratio was obtained to determine the destructive edge loading.
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