【摘要】 首先给出了定常温度热弹性Biot通解的一种新的简化形式,它看起来与各向同性弹性力学的Papkovich-Neuber通解十分相似。不作预先假设,从热弹性理论出发,利用Biot通解和Lur’e算子方法构造了梁的精化理论,得出了自由表面热弹性梁的三个精确方程:四阶方程、超越方程和温度方程。由一般的各向同性弹性梁推广到热弹性梁,导出了在反对称载荷和介质温度作用下热弹性梁的近似控制微分方程。更多还原

【Abstract】 A new simplified form of Biot’s thermoelasticity solution is presented under steady temperature,and it looks like Papkovich-Neuber’s isotropic elasticity solution.Based on thermoelasticity theory,the refined beam theory is derived using Biot’s solution and Lur’e method without ad hoc assumptions.For homogeneous boundary conditions,the thermoelastic beam equations consist of three exact equations: the four-order equation,the transcendental equation and the temperature equation.Generalized from isotropic elastic beam problems,thermoelastic beam problems are focused.Approximate beam equations under anti-symmetrical transverse loadings and temperature distribution are derived.更多还原