This work presents analytical solutions for bending deformation and stress distributions in functionally graded beams with arbitrarily and continuously variable thicknesses and resting on a two-parameter Pasternak elastic foundation. Based on two-dimensional elasticity theory directly, the general solutions of displacements and stresses which completely satisfy the differential equations governing the equilibrium for arbitrarily varying thickness functionally graded beams are derived for the first time. The undetermined coefficients in the general solution are obtained using Fourier series expansion along the upper and lower surfaces. The accuracy and efficiency of the proposed method are verified through several typical examples. The effects of mechanical and geometry parameters on the stress and displacement distributions of varying thickness functionally graded beams resting on a two-parameter Pasternak elastic foundation are discussed further.

中文翻译：

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两参数弹性基础上任意厚度变化的功能梯度梁的精确解

这项工作提出了具有任意和连续可变厚度的功能梯度梁中弯曲变形和应力分布的解析解，并位于两参数 Pasternak 弹性基础上。直接基于二维弹性理论，首次推导出了完全满足任意厚度函数梯度梁平衡微分方程的位移和应力的通解。通解中的未定系数是使用沿上下表面的傅立叶级数展开获得的。通过几个典型实例验证了所提方法的准确性和有效性。