夹 芯 梁 的 精 确 解 法

Exact Solution of Sandwich Beams

夹芯梁与普通梁的本质区别在于剪切引起芯层横截面严重的而又不均匀的翘曲变形，其应力分布已远非初等理论所能描述，而正在广泛应用的经典夹层理论却都建立在平面假设基础上，尤其不能正确反映弱芯的轻质夹层结构的行为，本文放弃了不合理的假设，将夹芯梁视为一般层状弹性体，严格按弹性理论导出了既满足控制方程又同时满足全部边界条件、层间的应力及位移的连续条件的封闭解。它可确切地反映夹芯梁的位移形态和应力分布，并从不同角度，包括多种实验和ＦＥＭ数值解，验证了它的正确性。

Seriously non-uniform warping cross sections due to shear effects sharply expose the essential difference between solid and sandwich beams. Actually,the deflected configuration and stress distributions in sandwich beam are far beyond the scope that the elementary bending theory is applicable for their description. For analysis of sandwich beams, the most extensively amployed classical theories are based on such assumption as the whole cross section or each individual layer thereof remains plane for bent configurations.As a matter of fact,theories based on such assumptions appear particularly incapable of depicting the mechani- cal characteristic behavior of sandwich beams,with a weak core in particular. Not relying on any assumptions,the present work tends to have the sandwich beam considered as layered elastic continuum. Close solution thereupon obtained satisfies the governing equations, the boundary conditions,as well as the stress continuitv and displacement compatibility requirements on interlayer interfaces. Experimental studies and numerical(finite element analysis)examinations fa- vorably justify the validity of the present solution together with its superb capa- bility of representing the displacement responses and stress distributions in sand- wich beams.