Strain-stress parametric analysis of structurally anisotropic panels of composite materials with account for manufacturing technology in MALAB

Mathematica modeling, numerical technique and program complexes


Gavva L. M.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



The paper discusses the stress-strain state of flat rectangular laminated panel from composite materials, which casing is eccentrically supported by the longitudinal-transverse stiffening set. The panel is subjected to arbitrary distributed transverse load per unit area in the stationary temperature field. Boundary conditions on the contour are assumed of quite general type.

The following technological factors occurring during the composites manufacturing herein should be taken into consideration: residual thermal stresses arising during cooling after hardening, and pre-stressed tension in reinforcing fibers.

Schematization of the panel as structurally anisotropic, when thin-walled reinforcing elements are in the complex resistance, was proposed as a design model. Further development of the theory of thin-walled elastic rods, related to the contact problem for the skin and the rib, with the refinement of the above said model reflects the scientific novelty of the research.

The problem of determining strain-stress state of structurally anisotropic panels is reduced to the solution of the boundary value problem for equation of the eighth order in the partial derivatives in a rectangular field. The resolved eighth order equation and natural boundary conditions are obtained with Lagrange variation procedure. The solution in closed form is constructed by unitary trigonometric series for the particular case of conformable boundary conditions on two opposite sides, and by the method of uniform solutions for arbitrary non-conformable boundary conditions at the contour. We examine all possible variants of the boundary edges restrictions in relation to the connecting plane problem and the bending one.

Computer software package has been developed in MATLAB for multi-criterion optimization for the design of structurally anisotropic composite panels of FA. Since the solution obtained by exact analytical methods, the calculation time was minimized, that is of interest from the viewpoint of practical design using parametric analysis. The results of the stress analysis calculations offer the possibility for reducing and optimization of the aircraft elements’ weight characteristics.


panels of composite materials, eccentric longitudinal and lateral set, thin-walled rib, asymmetric package structure, powered and temperature loading, Lagrange variation principle, strain-stress state, MATLAB


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