Superimposed Loads

Moment and out-of-plane shear loads due to significant pressure loads can only be captured in finite element analysis if the mesh is sufficiently fine. In most practical situations, a coarsely meshed “global loads” FEM is used for Sizing and Analysis. A global loads FEM may only have a few elements spanning a panel bay in either direction. In this situation, pressure-induced moments and out-of-plane shear loads imported into HyperX from the FEM will not be representative of the true stress-state of the panel. To address this, HyperX can import the value of the applied pressure from the FEM, perform the pressure analysis analytically, and superimpose the resulting pressure loads onto the primary loads imported from the FEM.

Methods used and applicable Advanced Settings differ based on whether the panel is flat or curved. You can access Advanced Settings from the Database tab of the Ribbon.

Flat

When pressure acts on a flat panel, out-of-plane shear and moment loads are induced, along with corresponding out-of-plane deflection, as shown in the figure below. These loads and deflections vary along both the length and width of the panel and are calculated depending on the boundary condition selected (Fixed or Simple). Because of this, loads at both the midspan and edge center of the panel are considered in all failure analyses. The worst combination of superimposed pressure load (midspan or edge center) and primary load (\(N_x\), \(N_y\), \(N_{xy}\), \(M_x\), etc.) are reported as the controlling load.

HyperX has several analytical methods available to compute the deflection, moment, and shear due to applied pressure. The method selected depends on the assumed boundary conditions, panel aspect ratio, and the panel orthotropic bending stiffness ratio (\(D_{11}/D_{22}\)). (See "Methods and Equations - Panel Pressure" linked below for more information on these methods).

Pressure loads can be applied as positive or negative values, with respect to the element +Z direction. There is an Advanced Database Setting ("Analyze positive and negative pressure moment superposition") to run the pressure loads in both positive and negative directions and return the worst case.

Curved

By default, pressure analysis is only applied to flat panels. To apply it to curved panels it must be enabled in Advanced Settings. There are three settings for customizing curved panel pressure analysis. The analysis methodology is based on SS8 Rayleigh-Ritz, see the "Methods and Equations - Panel Pressure" below for more information.

Beam-Column analysis is often referred to as a unique failure mode or even a buckling phenomenon. This is not strictly true. It is a geometric non-linear stress analysis that computes an additional moment (and shear) caused by the combined effect of in-plane compression and lateral deflection (eccentricity). The magnified moment is combined with FEA loads and affects local strength, crippling and local buckling margins.

For example, the figure below shows a beam under pressure \(P\). The pressure induces an initial 'lateral' deflection \(\delta\). Next, axial load \(N\) is applied. Because the beam has already deflected, the axial load induces an additional applied moment equal to \(N\delta\). This moment in turn induces even more lateral deflection \(\delta'\) denoted by the dashed lines. The key is that if the axial load was applied by itself, zero lateral deflection would occur.

In HyperX, the initial lateral deflection that triggers Beam-Column behavior can be due to applied pressure, assumed initial imperfection (given in length units at the midspan in the dialogue box), or applied end moments. The additional Beam-Column moments change the distribution of cross-section stresses and therefore requires updated margin of safety checks.

For more information see:

Users can choose to ignore FEA moments or transverse shear loads.

The Local Pressure toggle adjusts the superimposed panel pressure for skin objects of a stiffened panel. For pressure analysis, whether the loads are from FEA or user input, the local gradients of moment and shear transverse to the stiffener direction must be handled independently of the overall panel pressure solution. While the principal moments in the panel will be in the longitudinal direction (\(M_x\)), it is important to accurately capture the transverse moments (\(M_y\)) as well for analysis of the flange/facesheet joint (a bonded doubler joint).

A local curvature between stiffeners is caused by pressure on the skin object, and although the span distance between stiffeners is short (typically 2-6”) the facesheet is also relatively thin with a corresponding small bending stiffness. This results in local curvatures which must be considered in the strength analysis. This effect is included in HyperX's strength analysis by calculating the local curvature of each analysis object and superimposing that local curvature on the overall panel response.

For more information, see Section 7 of: