Calculation of singular field near the tip of a multi-material notch under thermal load with an over-determined method
This study presents an effective approach for analyzing the singularity of heat flux at the tip of a plane notch in multi-composite materials.By integrating the findings of singularity characteristics analysis with the finite element method,the thermally singular physical field at the notch tip is determined.Firstly,based on the Williams series expansion of the physical field near the notch tip,the characteristic equation of the thermal conduction singularity for the multi-composite material notch is derived.The singularity orders,characteristic angular functions,and their respective derivatives for the asymptotic expansion of the physical field at the notch tip are obtained by solving the characteristic equation numerically.Secondly,using a sparse finite element mesh,the temperature variation field near the notch tip is determined.The finite element results are then integrated with the singularity characteristics analysis results for constructing an over-determined system of equations.This system allows for the computation of the amplitude coefficients of the asymptotic expansion of the physical field near the notch tip,enabling the determination of the temperature variation field and the singular heat flux in the vicinity of the notch tip.The proposed method leverages the finite element computations with a sparse mesh,whereas high-precision computational results are obtained.The present method overcomes the reliance on dense meshes in conventional finite element methods for computing singular fields at notch tips,thereby enhancing computational efficiency.
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