求解层合板非线性屈曲问题一般方法的若干讨论

用广义傅立叶级数法建立具有弹性约束的复合材料层板在面内载荷作用下的非线性稳定性控制方程组后,讨论了非齐次项对方程组性质的影响,该非齐次项包含了所有的边界条件信息、外载信息及初始缺陷信息,可直接用作层板发生屈曲与否的判据。从数学上阐明了产生前屈曲耦合挠度的原因,并进一步从矩阵理论和非线性泛函两方面证明了前屈曲解的唯一性,进而提出了求解复合材料层板非线性稳定性问题的一般方法。

DISCUSSION ON THE GENERAL METHOD FOR SOLUTION OF NONLINEAR BUCKLING PROBLEMS OF LAMINATED PLATES

The nonlinear governing equations of composite laminated plates with edges elastically supported against rotation are established by the generalized Fourier series method. The influence of the inhomogeneous term of the equations is discussed. Since the inhomogeneous term contains all information of the boundary conditions, the applied load and the imperfection, it can be directly used in determining whether buckling will happen in the laminated plates. The causation to produce prebuckling coupling deflection is clarified in mathematics. The uniqueness of the prebuckling solution is proved with the matrix theory and the nonlinear functional knowledge, and the general way to solve the nonlinear stability problem of composite laminates is brought forward.