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HM Carbon Laminated Stiffness Analysis

Classical Laminate Theory analysis of stiffness, strain response, and ply stresses in a symmetric carbon laminate

PROJECT TYPE

Individual Project

MATERIAL

HM Carbon

METHOD

Classical Laminate Theory

YEAR

2026

01 / OVERVIEW

A laminate mechanics study evaluating how fiber orientation changes the stiffness, strain response, and internal ply stresses of a symmetric high-modulus carbon composite laminate.

The laminate consisted of multiple unidirectional carbon plies arranged symmetrically about the mid-plane.

Classical Laminate Theory was used to calculate effective engineering constants, laminate-level strains, and individual ply stresses while varying the fiber orientation angle θ.

02 / ANALYSIS OBJECTIVES

Evaluate the relationship between laminate architecture, fiber orientation, stiffness, and stress distribution.

  • Compute effective laminate engineering constants.
  • Determine laminate strains under the applied in-plane stress state.
  • Calculate stresses within each ply in the material coordinate system.
  • Evaluate how stiffness changes with fiber orientation angle θ.
  • Examine changes in Poisson ratios and deformation coupling.
  • Identify how ply orientation redistributes longitudinal, transverse, and shear stresses.
03 / LAMINATE CONFIGURATION

The laminate used a symmetric stacking sequence designed around a variable fiber angle θ and fixed ±30° plies.

STACKING SEQUENCE [ +θ / −θ / +30° / −30° ]s
E11 225 GPa
E22 7 GPa
G12 3.9 GPa
ν12 0.25

Each ply had a thickness of 0.0001 m, and the laminate was subjected to combined normal and shear loading.

04 / APPLIED LOADING

The laminate was evaluated under a combined in-plane stress state containing longitudinal, transverse, and shear components.

σxx 1799 MPa
σyy 282 MPa
τxy 672 MPa
05 / ANALYSIS METHOD

Classical Laminate Theory was used to connect individual ply properties to the effective behavior of the full laminate.

01 Material Properties

Define the orthotropic properties of the HM Carbon lamina.

02 Ply Transformation

Transform each ply stiffness based on its orientation within the laminate.

03 Laminate Stiffness

Combine ply behavior to determine effective laminate properties.

04 Stress Recovery

Calculate strain and recover individual ply stresses in material coordinates.

06 / CONTROL ANGLE RESULTS

Detailed laminate properties were evaluated at the assigned fiber orientation angle of 36.8°.

θ 36.8°

Assigned variable-ply angle

Exx 40,396 MPa

Effective x-direction stiffness

Eyy 10,227 MPa

Effective y-direction stiffness

Gxy 48,443 MPa

Effective shear modulus

At this orientation, the laminate remained significantly stiffer in the x-direction than in the y-direction.

07 / LAMINATE STRAINS

The applied stress state produced positive longitudinal strain, negative transverse strain, and a nonzero shear strain.

εxx 0.033375

Positive strain in the global x-direction.

εyy −0.04361

Negative strain in the global y-direction.

γxy 0.013872

Shear deformation resulting from the applied shear load.

08 / ORIENTATION EFFECTS

Rotating the fibers redistributed stiffness between the longitudinal, transverse, and shear directions.

Exx Highest at 0°

Maximum value: 145,075 MPa. Stiffness decreases as fibers rotate away from the x-direction.

Eyy Highest at 90°

Maximum value: 116,661 MPa. Transverse stiffness increases as fibers rotate toward the y-direction.

Gxy Maximum near 45°

Maximum value: 50,569 MPa. Shear resistance is greatest at an intermediate orientation.

09 / POISSON COUPLING

The effective Poisson ratios changed significantly with fiber orientation, showing that deformation coupling also depends on laminate architecture.

νxy MAX 2.0583

θ = 25°

νyx MAX 0.5572

θ = 55°

νxy MIN 0.1761

θ = 90°

10 / PLY STRESS DISTRIBUTION

Individual plies carried different portions of the applied load depending on their orientation.

Plies aligned closer to the primary loading direction developed larger longitudinal stress, while off-axis plies experienced stronger shear effects.

σ11 MAX 3942.94 MPa

θ = 25°

σ22 MAX 184.20 MPa

θ = 90°

τ12 MIN −286.64 MPa

θ = 40°

11 / ENGINEERING INTERPRETATION

Fiber orientation acts as a design variable that can redistribute stiffness and internal stress throughout a composite laminate.

Aligning fibers with the dominant loading direction increases stiffness and reduces deformation in that direction.

Rotating fibers away from the load shifts stiffness toward other directions and changes the longitudinal, transverse, and shear stresses carried by individual plies.

12 / ENGINEERING TAKEAWAY

The project demonstrated how laminate architecture can be intentionally tailored to achieve different structural responses.

Classical Laminate Theory provided a framework for predicting effective stiffness, deformation, and ply-level stress while accounting for the anisotropic behavior of the individual carbon plies.

The analysis reinforced the importance of fiber orientation when designing lightweight composite structures for specific aerospace loading conditions.

13 / FINAL DELIVERABLE

HM Carbon Laminate Analysis Presentation

The complete presentation includes laminate configuration, HM Carbon material properties, applied loading, analysis methodology, engineering constants, strain results, Poisson ratios, ply stresses, orientation sweeps, discussion, and conclusions.

FINAL PRESENTATION Open Full Screen ↗