On the equations of motion of shells in the reference state

Strain measures and compatibility equations in the linear high-order shell theories

“…Comparison of (44) with (21) and (14) allows us to conclude that, with the exception in (44) of some scale factors and of the underlined terms, the corresponding expressions for the nth-order strain measures are formally similar one another. Moreover, this formal similarity entails the conclusion that the general form of compatibility equations as deduced in Sec.…”

“…In order to express them explicitly in terms of the selected strains, we differentiate covariantly (23ŵ ith respect to x", multiply the result by exd and use Mainardi-Codazzi equations and also (14)3. This yields | ys ~ bya Jpl | s+ ("+ 1 )byay%+11 + bw bpd -/3"\ -(nbya b} V[n)), J = 0 (n = 0, N), (24) which again contains the displacement V[n).…”

Refined geometrically nonlinear theories of anisotropic laminated shells

“…The basic field equations derived in Sections 6.1-6.5 may easily be specialized for this case. Some results pertaining to this theory are reported in [25,5,32,[40][41][42][43]. Moreover, a large diversity of high-order theories may result through various selection of ^in (14).…”