Abstract The response of a disk made from a heterogeneous material within the framework of Lord-Shulman theory is investigated in this article. The theory admits a single relaxation time to avoid the infinite speed of temperature wave. It is assumed that all of the thermomechanical properties except for Poisson ratio and thermal relaxation time vary exponentially through the radial direction of the disk. Two coupled equations, namely, the axisymmetric equation of motion and the energy equation are obtained for the disk. The energy equation is kept in the nonlinear form and the linearization of the previous investigations is not performed in this work. These two equations are provided in a dimensionless presentation. After that, using the generalized differential quadrature method, a system of nonlinear algebraic equations is established. Following the Newmark time marching method, the temporal evolution of radial displacement and temperature at the nodal points of the disk are obtained. Comparison study is given to assure the validity of the proposed solution method. After that, novel numerical results are given to discuss the effects of involved parameter. It is shown that, under the nonlinear analysis, the magnitudes of radial and hoop stresses and radial displacement are underestimated.

中文翻译：

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使用 Lord-Shulman 模型的指数梯度盘的热非线性响应

摘要 本文在 Lord-Shulman 理论框架内研究了由异质材料制成的圆盘的响应。该理论承认单一弛豫时间可以避免温度波的无限速度。假设除泊松比和热弛豫时间之外的所有热机械特性在圆盘的径向上呈指数变化。得到了圆盘的轴对称运动方程和能量方程两个耦合方程。能量方程保持非线性形式，并且在这项工作中不进行先前研究的线性化。这两个方程以无量纲表示形式提供。之后，利用广义微分求积法，建立了非线性代数方程组。遵循Newmark时间推进方法，获得了圆盘节点处径向位移和温度的时间演化。给出了比较研究，以确保所提出的求解方法的有效性。之后，给出了新的数值结果来讨论所涉及参数的影响。结果表明，在非线性分析下，径向和环向应力以及径向位移的大小被低估了。