Abstract
Fundamental solutions and their derivatives located along fibre axes are presented to simulate the interactions of matrix and reinforcing elements in composite materials, when the primary field is a scalar function temperature in heat conduction. The inter-domain continuity is specified in discrete points on fibres boundaries. Intensities of the source functions are defined by 1D NURBS (Non-Uniform Rational Basis Spline) and computed in LS (Least Square) sense in the fibres. The inter-domain continuity equations have to be completed by balance equations (energy, equilibrium, etc.) in order to obtain temperature in centre of each fibre. Gradients of temperature are supposed to be constant in cross-sections of the fibres and are computed iteratively by considering them to be linear along fibres in the first step. Material properties of both matrix and fibres are assumed to be homogeneous and isotropic. Three numerical examples giving two fibres overlapping in some lengthin infinite matrix show the numerical behaviour of the problem for heat conduction.
Highlights
In past decades, fibre-reinforced composites have been widely used in engineering applications due to the superiority of their electro-thermo-mechanical properties over the single matrix
The interaction of fibres with matrix is simulated in the Method of Continuous Source Functions (MCSF) by source functions which are 1D-continuously distributed along the fibre axis
The MCSF is a kind of Method of Fundamental Solutions (MFS) which uses a fundamental solution and its derivatives to simulate the interaction of short fibres with matrix
Summary
Fibre-reinforced composites have been widely used in engineering applications due to the superiority of their electro-thermo-mechanical properties over the single matrix. As for the BEM, elements are used to satisfy boundary conditions and the fundamental solutions (FS) are considered to be continuously distributed along the domain boundaries on elements being one dimension lower than the domain, the MFS is a meshless method using discrete source functions, FS, located outside the domain. The inter-domain boundary (compatibility) conditions and basic unknowns have to be specified so that good numerical stability is achieved It is realized by specifying field quantities (temperatures, displacements, strains) by difference of the value in a collocation point and that in a related point (centre of the fibre, or another point on a corresponding fibre cross-section boundary). The resulting system of equations is evaluated by the LS method This enables to satisfy the inter-domain boundary conditions in a cross-sectional direction with good numerical stability of the.
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