Scope and coordinates
Current Workbench pressure summary. The thin-wall pressure strain summary uses the complete inverse laminate extensional stiffness, including Poisson and extension–shear coupling: ε⁰ = A⁻¹N with curvature constrained to zero. Its x direction is axial and y is hoop. Open ends omit the pressure end-cap force, but axial Poisson contraction remains. This summary is not the general free-curvature ABD shell solution shown below, and it does not resolve radial stress or local end effects. Keep the separate layerwise thick-wall profile and supported ply-failure calculations distinct.
The shell route uses axial x, circumferential arc-length y = rmθ, and outward radial z coordinates. It is intended for thin-to-moderately-thick cylinders where a membrane-dominant sizing solution is appropriate. The laminate ABD matrix, environmental resultants, damage state, and density come from the same upstream solver used by the plate and beam branches.
Equation detailsExplanation · variables · model connection · reference+
Converts the pressure difference across a closed-end cylinder into hoop and axial membrane force per unit length.
Model connectionThese pressure terms enter the common laminate resultant vector before constitutive recovery.
Theory basisCDS online structural theory, structural geometry module
Equation detailsExplanation · variables · model connection · reference+
Superimposes user-applied axial force and torque on the pressure-generated membrane actions.
Model connectionThe load-scaler inputs remain independent of geometry and are transformed into the shell resultant basis here.
Theory basisCDS online structural theory, cylinder loading
Equation detailsExplanation · variables · model connection · reference+
Uses the active laminate ABD matrix to recover mid-surface strain and curvature after mechanical and environmental resultants are combined.
Model connectionRecovered ply strains and stresses feed the selected failure and progressive-damage models.
Theory basisCDS hygrothermal CLT and ABD theory
Radial response and outputs
For the membrane shell path, the mean radial displacement is recovered from the hoop strain as w ≈ rmεy. Named results provide the cylinder summary, pressure, force, torque and resultant histories, plus the final radial-coordinate and recovered-stress table.
Assumptions and limits
- Axisymmetric constant circular section with small strains and small displacement.
- Membrane-dominant response; local end effects, ovalization, openings, and geometric imperfections require higher-fidelity analysis.
- Closed-end axial pressure force is included only when the selected end condition requires it.
- Use the Hyer route when through-wall radial stress and layer-interface traction continuity are important.
Workbench availability: released models, inputs and compatible study paths. The wider theory library includes reference formulations not available in every Workbench solve.