Features > Materials > Discrete Laminates > Laminate Analysis Form

Laminate Analysis and Equivalent Effective Properties Form

The Laminate Analysis form opens by clicking the Analyze button on the Laminate Editor form. This form performs the following actions:

Generates laminate stiffness properties using classical lamination theory.
Given a failure theory, generates effective laminate allowables (F_u1, e_u1) and a failure envelope (N_x vs. N_y).
Given an applied load state and failure theory, plots ply-by-ply failure, stresses, strains, and margins of safety corresponding to the applied load state.

Options

The Options frame on the left side determines the results on the right.

Tension vs. Compression vs. Average Determines which ply stiffness properties to use when computing the overall laminate stiffness.
Limit vs. Ultimate This option affects isotropic plies only. It determines which isotropic allowables (limit or ultimate) to use when generating the failure criteria.
Reference Plane Location When computing the overall laminate stiffness, a reference plane must be specified. Typically the reference plane is taken at the midplane of the laminate. Using these options, the reference plane can be specified relative to the laminate thickness at the outer fiber, midplane, or inner fiber. Also, an additional offset can be specified in the Reference Plane Offset box.

The equations below describe the effect that a change in reference plane (Δz) has on the ABD matrices. The membrane stiffness does not change (A' = A), but the bending and bending-coupling matrices are heavily influenced by the offset. These relationships apply to the stiffened panel ABD matrices as well.

A' = A

B' = B + ΔzA

D' = D + 2Δz B + Δz²A

User Defined / Allowable Load User-defined membrane and bending loads are applied here. These loads are applied at the reference plane defined using the above options.

Once a user-defined load is entered, the allowable load in the neighboring cells is updated. Also, the results in the Failure Analysis, Strain Plot, Stress Plot, and MOS Plot tabs are updated. The Failure Envelope tab is not affected by the user-defined load.
Failure Theory The choice of failure theory effects what criteria is used to generate the:
- Allowable load (next to the user-defined loads in Options frame)
- Failure Analysis tab and MOS Plot tabs
- Failure Envelope tab
- Effective laminate failure allowables
Show Minimum MOS Analysis Only If selected, the Failure Analysis tab will only show one entry per ply corresponding to the lowest margin of safety. If cleared, each ply will have three entries corresponding to the top, bottom and middle of the ply.
Ref Temperature This is the temperature at which the ply material properties are taken. The default temperature is 72° F.

To add another temperature to the list, type the temperature in the box and press [Enter].

If an effective laminate is created, material properties will be generated for each temperature in this list.
Outer/Midplane/Inner Fiber Delta T Specifies through-thickness changes in temperature at the inner, midplane, and outer fibers. Changes are taken to the reference temperature (above). Given these three temperature points, the final temperature distribution is linearly interpolated through the thickness.

The final temperature at each ply is the temperature at which material properties are taken. The analysis will not compute thermally induced ply stresses and strains. However, if the analysis is done in the Sizing form, thermally induced ply stresses and strains will be captured.

Output Properties

Stiffness Terms Classical lamination theory ABD matrix. Only isotropic and orthotropic plies are analyzed. All other materials are treated as empty space.
Effective Laminate Elastic and Flexural Elastic Engineering Constants See Effective Laminate Elastic Properties.
Neutral Axis See Effective Laminate Elastic Properties.
Effective Laminate Failure Allowables See Effective Laminate Allowables.

Output Tabs

Failure Analysis Based on the user-defined load and failure theory, this tab shows the ply-by-ply margin of safety for the top, middle, and bottom of each ply.

Strain, Stress, and MOS Plot Based on the user-defined load and failure theory, shows stresses, strains, and margins of safety for the top, middle, and bottom of each ply. These data can be displayed for only the middle of each ply as well.

Stresses and strains are output in the 1 (0°), 2 (90°), and 12 (shear) directions. Stress and strain data can be exported to a CSV (comma-separated file) and directly opened in Excel.
Failure Envelope Based on the user-defined failure theory only, this tab shows the failure envelope, N_x vs. N_y, for three levels of applied shear. The failure envelope is generated in 15 degree increments.

Zoom in by left-clicking and creating a box and reset view by right-clicking.

The percentage shear is normalized by the vector magnitude of the N_x, N_ycoordinate pair.