When buckling a plate of two ends fixed, the deflection equation of the plate can be expressed by: y=y0*(1-cos mx) where the maximum deflection at the center is 2*y0. With this equation, the cross sectional area and the young's modulus of the plate is usually unchange.

However, if the plate have three segments of flexural rigidity along the bending axis. The middle segment is thicker and have a far higher young's modulus than the other two segments, it is found that the deflection at the middle segment is flattened a little bit. The equation: y=y0*(1-cos mx) seems not fit this situation.

Would you give me some hints on how to calculate the deflection of the plate in this case, please? Thank you so much for your help!

Best regards,

Tracy

Draw the M/EI diagram. Because E is larger at the mid-segment, the diagram will drop at the point of intersection of the segments. You can then find the deflection by using the concept of deviation.