Bend stiffeners are subjected to cyclic loading during offshore operation or when subjected to a controlled full-scale qualification test. Due to the viscoelastic nature of the polyurethane, energy is dissipated within the material volume and the structure may experience a temperature increase, a phenomenon known as self-heating. The top connection is a flexible riser critical region in terms of fatigue, being the bend stiffener the main responsible for curvature control. As the curvature distribution is highly affected by the nonlinear time–temperature bend stiffener response, a detailed thermo-mechanical assessment may become relevant for riser lifetime and polyurethane material failure assessment, specially during accelerated full-scale tests. In the present paper (Part I), the polyurethane experimental characterization and steady-state thermo-mechanical mathematical formulation are presented for the bend stiffener self-heating assessment. A steady-state formulation is derived for a temperature dependent linear viscoelastic large deflection beam model to estimate the heat generation during harmonic tip loading. The temperature field distribution is calculated through a three-dimensional steady-state thermal model considering the viscoelastic heat calculated from the mechanical model with an iterative scheme. Stress relaxation tests are performed at different temperatures to determine the viscoelastic properties followed by thermal properties characterization through differential scanning calorimetry and by the Flash method to determine the specific heat, thermal conductivity and diffusivity, respectively. In a companion paper (Part II) the iterative numerical scheme is detailed and a case study presented.

弯曲加劲肋在海上作业期间或在进行受控的全尺寸合格性测试时会承受周期性载荷。由于聚氨酯的粘弹性，能量在材料体积内耗散，结构可能会经历温度升高，这种现象称为自热。就疲劳而言，顶部连接是柔性立管的关键区域，是弯曲加劲件，主要负责曲率控制。由于曲率分布受非线性时间-温度弯曲加劲肋响应的影响很大，因此详细的热机械评估可能与立管寿命和聚氨酯材料失效评估相关，尤其是在加速的满量程测试期间。在本文（第一部分）中，提出了用于弯曲加固件自热评估的聚氨酯实验表征和稳态热力学数学公式。为温度相关的线性粘弹性大挠度梁模型导出稳态公式，以估算谐波尖端加载过程中的热量产生。温度场分布是通过三维稳态热模型计算的，其中考虑了通过迭代方案从机械模型计算出的粘弹性热量。在不同温度下进行应力松弛测试，以确定粘弹性，然后通过差示扫描量热法和闪速法分别确定比热，导热率和扩散率，以表征热性能。