The laminate plate theory formulates the strain having the origin of the coordinate system at the mid-plane. If I have a complex structure, could I divide it into several plates (may not be at the same orientation relative to one another) and transfer the individual laminate (local) coordinate systems to a global coordinate system? So, similarly to parallel axis theorem used to find the moment of inertia, could I use the same concept for the structure stiffness matrix? My final goal is to determine the natural frequency of the structure.
Thanks in advance,
Hello, at first, parallel axis theorem is valid for laminate analysis, even we calculate Q values and stiffness matrices by using parallel axis theorem by using the position information of indivudial laminae and its distance from plate midplane. In a complex structure as you mentioned you may be divide it into various laminates and then combine them together. But I could not remember any specific example or study. Sincerely.
Hello, you may take the origin of the z-axis at any position. According to the straight normal hypothesis, used in the laminate theory, the in-plane displacement vector is a linear function of z. This, together with constitutive equations for individual layers, can be used to derive any parallel axis theorem.
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