Expert-level composites engineering covering fiber reinforced polymers, matrix materials, laminate theory, manufacturing processes, failure modes, and composite design.
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Carbon fiber: high stiffness and strength, low density, expensive, brittle. Glass fiber: lower stiffness than carbon, cheaper, good impact resistance. Aramid fiber: Kevlar, high toughness, good impact, poor compression. Epoxy matrix: most common thermoset, good adhesion, brittle, limited temperature. Thermoplastic matrix: PEEK, recyclable, tougher than thermoset, higher cost.
Rule of mixtures: E1 = Ef times Vf plus Em times Vm for longitudinal modulus. Transverse modulus: inverse rule of mixtures, matrix dominated. Longitudinal strength: fiber dominated, approximately Vf times sigma_f_ult. Fiber volume fraction: typically 55-65% for aerospace structural laminates.
ABD matrix: A membrane stiffness, B coupling, D bending stiffness. Ply angles: 0 for axial, 90 for transverse, plus minus 45 for shear. Symmetric laminate: B = 0, no bending-extension coupling. Balanced laminate: equal plus and minus angle plies, no shear-extension coupling. Failure criteria: Tsai-Wu or Tsai-Hill for ply-level failure prediction.
Hand layup: manual ply placement, low cost, labor intensive, variable quality. Autoclave cure: high pressure and temperature, aerospace quality, expensive. RTM: resin transfer molding, inject resin into dry fiber preform. Filament winding: continuous fiber wound over mandrel for pressure vessels and pipes. AFP and ATL: automated fiber placement and tape laying for large structures.
| Pitfall | Fix |
|---|---|
| Applying isotropic analysis to anisotropic laminates | Use laminate theory for accurate stiffness prediction |
| Ignoring compression strength reduction | CFRP compression strength much lower than tension |
| Wrong cure cycle causing residual stress | Follow manufacturer cure cycle exactly |
| No impact damage assessment | BVID dramatically reduces compression strength |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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