Stiffened panels#

panels models stiffened panels in two ways:

  • a StiffPanelBay, a skin with blade stiffeners BladeStiff1D or BladeStiff2D along \(x\), whose skin panels and stiffener bases share the Ritz constants of the skin, a compact model for the global buckling, vibration and flutter of the bay;

  • a MultiDomain assembly, in which the skin, the bases and the flanges are plate domains connected to each other, e.g. the panel with a T-stiffener of panels.multidomain.tstiff2d_1stiff_compression, see Multi-domain assemblies, which also represents debonding defects between the skin and the base, following Castro and Donadon [castro2017Multidomain].

Stiffened panel bay#

The bay is a rectangular plate or cylindrical panel, \(0 \le x \le a\), \(0 \le y \le b\), with the attributes a, b, r, model, the laminate (stack, plyt, laminaprop, rho), the numbers of terms m and n, and the flags of the boundary conditions of its four edges, see Boundary conditions, by default with \(u\), \(v\) and their slopes and \(w\) removed on all edges and the slopes of \(w\) free. Only the models with 3 degrees of freedom per term, based on the classical laminated plate theory, are supported.

The skin is divided along \(y\) into panels with StiffPanelBay.add_panel(), each a Shell that spans the whole bay with the approximation functions and the boundary conditions of the bay, but is integrated only over its strip \(y_1 \le y \le y_2\), see Shell.integration_limits(); each panel may have its own laminate and stress resultants Nxx, Nyy, Nxy. The displacement field of the skin is therefore continuous without any connection, and the matrices of the bay are the sums of those of the panels and of the stiffeners.

The stiffeners are added after the panels, at a coordinate \(y_s\), with StiffPanelBay.add_bladestiff1d() or StiffPanelBay.add_bladestiff2d(). Both may have a base, a Shell bonded below the skin with its offset, using the Ritz constants of the skin, and a flange:

  • BladeStiff1D: the flange is a beam along \(x\) whose displacements are those of the skin along \(y = y_s\), which adds no degree of freedom, and whose local buckling is not represented;

  • BladeStiff2D: the flange is a plate with its own mf by nf terms, connected to the base, or to the skin, by penalty stiffnesses, which represents its local buckling, see StiffPanelBay.get_size().

The matrices StiffPanelBay.calc_kC(), StiffPanelBay.calc_kG(), StiffPanelBay.calc_kM(), StiffPanelBay.calc_kA() and StiffPanelBay.calc_cA(), and the vector StiffPanelBay.calc_fext() are solved with structsolve as those of a Shell, e.g. lb(bay.calc_kC(), bay.calc_kG()). The displacements of the skin and of the stiffeners are calculated with StiffPanelBay.uvw_skin() and StiffPanelBay.uvw_stiffener() and plotted with StiffPanelBay.plot_skin() and StiffPanelBay.plot_stiffener(). The flutter of the bay with the piston theory is described in Panel flutter with the piston theory.

The construction of a bay and the linear buckling analyses are shown in Stiffened panel bays.