When buckling plate of both ends fixed, the deflection and the mode shape of the plate can be found from the equation: y=M(1-cos mx)/P. With this equation, the cross sectional area and the young's modulus of the plate is usually unchange. However, if the flexural rigidity of the plate is divided into three segments such that the middle segment have a higher flexural rigidity than the other two segments, it is found that the equation: y=M(1-cos mx)/P seems not fit this situation. Would you know how to calculate the deflection and the mode shape in this case, please? Thank you in advance.