# Finite-Layer Method: a Unified Approach to a Numerical Analysis of Interlaminar Stresses, Large Deflections, and Delamination Stability of Composites Part 1. Linear Behavior

A new method for a stress–strain analysis of layered composites, named the finite-layer method, is proposed, which is based on the consideration of each particular layer as a constituent of the entire laminate. This method serves as a unified approach to the development of new algorithms for computing stresses in composite layers, interlaminar contact stresses, large deflections, and critical buckling loads of thin-walled laminated structures with delaminations. The calculation of a laminated structure is reduced to solving a boundary-value problem for a system of first-order ordinary differential equations. The number of equations depends on the number of layers in the composite. The resolving system of differential equations is a stiff system. The stable numerical method of discrete orthogonalization is used for solving the boundary value problem. Part 1 is dedicated to the application of the proposed method to a linear analysis of free-edge stresses in composite laminates, to a study of the deformation of composite plates with delaminations and bending of composite beams with patches, and to calculations of adhesive joints.

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Correspondence to A. M. Timonin.

Translated from Mekhanika Kompozitnykh Materialov, Vol. 49, No. 3, pp. 339–356 , May-June, 2013.

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Timonin, A.M. Finite-Layer Method: a Unified Approach to a Numerical Analysis of Interlaminar Stresses, Large Deflections, and Delamination Stability of Composites Part 1. Linear Behavior. Mech Compos Mater 49, 231–244 (2013). https://doi.org/10.1007/s11029-013-9339-1

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### Keywords

• finite-layer method
• composite laminate
• deformation model
• interlaminar stresses
• delamination
• boundary-value problem
• stiff system of equations