<p>This study presents a finite element formulation for the static and free vibration analysis of truncated conical laminated composite shells (TCLCSs) using the Carrera unified formulation (CUF). The CUF offers a robust and flexible modeling framework that incorporates the equivalent single-layer (ESL) approach using user-defined higher-order polynomial expansions. This flexibility enables accurate representation of displacement fields across the thickness, capturing both global and local behaviours in thin and moderately thick TCLCSs. The governing equations are derived using the principle of virtual displacement (PVD), considering only elastic and inertial forces to model undamped free vibrations. Displacement fields are expanded in the thickness direction using Taylor series polynomials, allowing systematic control over the level of approximation. The developed finite element model, incorporating curved isoparametric shell elements, accurately captures the geometric complexities and effectively integrates orthotropic material properties typical of laminated composites. The proposed formulation using the CUF has a good agreement with previous benchmark studies. The maximum differences in non-dimensional transverse displacements are up to 7.4%, and the maximum differences in non-dimensional stresses are limited to 7.2%. The maximum difference in non-dimensional natural frequencies is also around 2.4%. Considering all validation cases, the average variation is around 3.3%, highlighting the reliability and accuracy of the proposed model for TCLCSs. Comprehensive parametric studies are conducted to investigate the influence of key design parameters, including boundary conditions, slenderness ratio <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$(L/h)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>L</mi> <mo stretchy="false">/</mo> <mi>h</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, vertex angle <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$(\beta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, conical length <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$(L)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>L</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, conical base radius <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$ \left( {R_{1} } \right) $</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <msub> <mi>R</mi> <mn>1</mn> </msub> </mfenced> </math></EquationSource> </InlineEquation>, fibre orientation <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$(\theta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, and lamination schemes such as cross-ply and angle-ply. The results demonstrate that CUF is a robust and efficient tool for capturing the static and free vibration responses of TCLCS, supporting its suitability for the optimal design of advanced composite structures in aerospace, marine, and automotive applications.</p>

A CUF-Based Finite Element Model for the Structural Behaviour of Truncated Conical Laminated Composite Shells

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发表日期：

2025年12月29日

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Satish Sahu,
Rajana Suresh Kumar

摘要

This study presents a finite element formulation for the static and free vibration analysis of truncated conical laminated composite shells (TCLCSs) using the Carrera unified formulation (CUF). The CUF offers a robust and flexible modeling framework that incorporates the equivalent single-layer (ESL) approach using user-defined higher-order polynomial expansions. This flexibility enables accurate representation of displacement fields across the thickness, capturing both global and local behaviours in thin and moderately thick TCLCSs. The governing equations are derived using the principle of virtual displacement (PVD), considering only elastic and inertial forces to model undamped free vibrations. Displacement fields are expanded in the thickness direction using Taylor series polynomials, allowing systematic control over the level of approximation. The developed finite element model, incorporating curved isoparametric shell elements, accurately captures the geometric complexities and effectively integrates orthotropic material properties typical of laminated composites. The proposed formulation using the CUF has a good agreement with previous benchmark studies. The maximum differences in non-dimensional transverse displacements are up to 7.4%, and the maximum differences in non-dimensional stresses are limited to 7.2%. The maximum difference in non-dimensional natural frequencies is also around 2.4%. Considering all validation cases, the average variation is around 3.3%, highlighting the reliability and accuracy of the proposed model for TCLCSs. Comprehensive parametric studies are conducted to investigate the influence of key design parameters, including boundary conditions, slenderness ratio $(L/h)$ $(L / h)$ , vertex angle $(\beta )$ $(β)$ , conical length $(L)$ $(L)$ , conical base radius $ \left( {R_{1} } \right) $ $(R_{1})$ , fibre orientation $(\theta )$ $(θ)$ , and lamination schemes such as cross-ply and angle-ply. The results demonstrate that CUF is a robust and efficient tool for capturing the static and free vibration responses of TCLCS, supporting its suitability for the optimal design of advanced composite structures in aerospace, marine, and automotive applications.