Composite Structural Analysis

Deflection, stress, and buckling analysis for composite beams, sandwich panels, plates, and cylinders using CLT stiffness data.

Overview

The structural analysis tools take your laminate's CLT stiffness properties (from the ABD matrix) and apply them to common structural elements. Each tool calculates deflections, stresses, and buckling loads for a specific geometry under your chosen loading and boundary conditions, and each has its own reference page with the formulas, validity limits, and design guidance: beam, sandwich panel, plate, and cylinder.

All structural tools share the same workflow:

1. Select a laminate from your saved laminates, or define a quick custom layup directly on the page.
2. Enter geometry: dimensions specific to the structural element (length, width, radius, etc.).
3. Define loading: choose boundary conditions, load type, and magnitude.
4. Read results: deflections, stresses, safety factors, and buckling loads update in real time.

The beam, plate, and cylinder tools use CLT stiffness data only and do not perform strength-based ply failure checks; for ply-level strength assessment, use the First Ply Failure tool alongside the structural analysis. Sandwich construction is the exception, on the plate and on the beam: it also checks facesheet first ply failure (Maximum Stress criterion) when the facesheet laminate carries strength data.

Beam / Column

Analyses a composite beam under transverse loading, and reports its column buckling capacity alongside it for when the same member is loaded axially. Nine cross-sections cover the rectangular strip, round tubes, boxes, open shapes and a sandwich of two facesheets on a core, with bending and shear stiffness from the laminate's CLT terms. Deflection includes the shear part, and the buckling load is shear-reduced. Four boundary conditions and three load types cover the common cases. The sandwich section adds the core's shear and four local checks with a safety factor each. See the full beam analysis reference for the formulas and the boundary condition coefficients.

The beam tool, with bending and Euler buckling results for one laminate.

Sandwich Panel

Sandwich is a construction of the plate tool: the same rectangular plate, any edge free, simply supported or clamped, under pressure, a patch load or combined in-plane loads, built from two composite facesheets on a lightweight core. Each result is shown beside the same panel with a rigid core, which shows the core's shear flexibility, and every sandwich failure mode (facesheet stress, core shear in x and y, face wrinkling, core crushing, shear crimping) gets its own safety factor so the governing one is visible at a glance. Core materials (honeycomb, structural foam, balsa) live in your material library with presets to start from, and honeycomb takes separate ribbon and transverse shear values. See the full sandwich panel analysis reference for the formulas, the failure modes, and core selection. For a sandwich strip on supports, use the sandwich beam tool, which shares the same facesheet and core.

Sandwich panel analysis, with a safety factor per failure mode.

Plate

Analyses a rectangular composite plate by the Ritz method, from the laminate's full D-matrix including the bending-twisting terms, with transverse shear included. Each edge is free, simply supported or clamped. Buckling takes any combination of N_x, N_y and N_xy; deflection takes a uniform pressure plus an optional square patch load and reports the bending moments, next to the same plate solved as a thin plate. Every result carries its own convergence check, and three D-matrix treatments cover unsymmetric laminates and comparison with specially orthotropic textbook values. See the full plate analysis reference for the Ritz formulation, the edge conditions, and the convergence check.

The plate tool, with a condition per edge and a convergence check on every result.

Tube / Cylinder

Analyses a thin-walled composite cylinder for membrane stresses, torsional properties, and buckling under five load cases: internal and external pressure, axial compression, torsion, and bending. Buckling results always pair the classical value with an empirical knock-down factor (NASA SP-8007 for axial compression and bending), because classical shell theory overestimates capacity by 2 to 5 times. See the full tube and cylinder analysis reference for the formulas, the load cases, and the knock-down factors.

The cylinder tool under external pressure, knock-down factor visible.

Force & Moment Resultants

Every structural tool has a Resultants tab reporting the force and moment intensities the analysed structure carries at its critical location, per unit width: N_x, N_y, N_xy, M_x, M_y, M_xy. Reading resultants per unit width is what makes a structural result comparable to a laminate result, and it is exactly what the laminate analysis tools take as input. That closes the loop between sizing a structure and checking the plies inside it.

Values are signed in the same Classical Lamination Theory convention the analysis tools use: tension positive, compression negative, z positive upward. Where the physics has more than one critical location, a selector picks between them.

Use as analysis loads in the results panel header writes the vector into the mechanical load vector shared by Laminate Load, First Ply Failure, Ply Stresses & Strains and Progressive Failure, so there is no need to derive N and M by hand. It copies a snapshot rather than creating a live link: a chip on the analysis pages records where the loads came from, and clears as soon as you edit a load value yourself.

The beam tool's Resultants tab. M_x is negative because the load sags the beam, putting the top surface in compression.

Buckling loads and pressures are stability thresholds rather than stress states, so they never appear as resultants and are never copyable, since running a ply failure check on an eigenvalue is meaningless.

Safety Factors

The plate, cylinder, and sandwich panel tools report safety factors using the same color-coded scheme as the failure criteria tools. The beam tool reports deflection, stress, and buckling values directly, without a safety factor, except on the sandwich section, whose local checks use the same scheme:

• Green (SF ≥ 1.5): comfortable margin above failure or buckling.
• Amber (1.0 ≤ SF < 1.5): safe but with limited margin. Review loading assumptions.
• Red (SF < 1.0): the applied load exceeds the predicted failure or buckling load.

Assumptions & Limitations

The structural analysis tools are aimed at preliminary sizing and trade studies. What they assume:

• Linear elastic analysis. All tools assume small deformations and linear material behavior. Nonlinear effects (large deflections, material degradation) are not captured.
• CLT-based stiffness. Laminate properties come from Classical Lamination Theory, which assumes thin plies with perfect bonding (no delamination).
• Simplified geometry. Beams are prismatic with one of nine standard cross-sections, plates are flat and rectangular, cylinders are circular. Complex shapes require FEA.
• Analytical and series solutions, not FEA. The beam and cylinder tools use closed-form formulas, most accurate for simple loading and boundary conditions. The plate tool, sandwich panels included, solves a Ritz series and checks its own convergence.

Author: Rick Schrijver

References

1. Gere, J.M. & Timoshenko, S.P. (1997). Mechanics of Materials, 4th ed. PWS Publishing. ISBN: 978-0534934293. (Euler-Bernoulli beam theory and column buckling)
2. Zenkert, D. (1995). An Introduction to Sandwich Construction. EMAS Publishing. ISBN: 978-0947817760. (Sandwich panel theory, wrinkling, and failure modes)
3. Reddy, J.N. (2004). Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed. CRC Press. ISBN: 978-0849315923. (Plate theory and the Ritz method for laminated plates) doi:10.1201/b12409
4. NASA. (1968). Buckling of Thin-Walled Circular Cylinders. NASA Space Vehicle Design Criteria (Structure), NASA SP-8007. ntrs.nasa.gov
5. US Department of Defense. (1968). Structural Sandwich Composites, MIL-HDBK-23A. (Core material properties, honeycomb and foam core design data, face wrinkling and core crushing)
6. Barbero, E.J. (2018). Introduction to Composite Materials Design, 3rd ed. CRC Press. Chapter 10. (Sandwich panel design and core selection) doi:10.1201/9781315296494

Frequently Asked Questions