Claude Skills by ashfordeOU

Use when you must predict the engineering constants of a unidirectional composite lamina from the fiber and matrix constituent properties and the fiber volume fraction: compute the longitudinal modulus E1 and the major Poisson ratio nu12 by the rule of mixtures, the transverse modulus E2 by the Halpin-Tsai closed form with the xi equal to 2 shape factor on the fiber transverse modulus, the in-plane shear modulus G12 by the Halpin-Tsai closed form with the xi equal to 1 shape factor on the fib...

Use when the task is bird strike impact analysis and certification of transport aeroplane structure per FAR 25.631 and CS-25: estimate the impact kinetic energy of a 4 pound or 8 pound bird at cruise velocity with impact_energy, convert the bird mass to kilograms with bird_mass_kg, compute the specific energy with specific_energy, and rate the strike against the component damage threshold with damage_severity_ratio, penetration_verdict, and residual_strength_fraction for the residual strength...

Use when you must calculate fatigue crack growth for damage-tolerant structure: estimate the mode I stress intensity factor at a crack, apply the Paris law crack growth rate, and project the cycles to grow the crack from the initial detectable size to the critical size. Produces the stress intensity factor, the Paris da/dN rate, the crack extension per cycle, and the cycles-to-critical estimate that feed residual strength and inspection interval assessments. Trigger: crack growth, stress inte...

Use when you must compute the residual strength of a cracked structure for a damage tolerance assessment: derive the residual strength from fracture toughness and crack length, find the critical crack length at which the applied stress reaches Kc, and evaluate the margin of the residual strength against the limit load. Produces the residual strength, the critical crack length, and the limit-load margin verdict that size inspection intervals and repair decisions. Trigger: residual strength, cr...

Use when you must compute the walker-forman-crack-growth rate of a mode I crack under a nonzero stress ratio in airframe structure: apply the walker-equation equivalent range dK_bar = dK/(1-R)^(1-gamma) with the material gamma exponent and the forman-equation rate da/dN = C_F*dK^m/((1-R)*K_c - dK) with the kc-limited denominator, then extend the crack over a stated cycle block at constant or piecewise stress ratio R. Produces the R-corrected rate table with the walker-equation and forman-equa...

Use when you must screen transport airplane structure for widespread fatigue damage (WFD) per FAR 25.571: classify multiple site damage (MSD) cracks in adjacent fastener holes and multiple element damage (MED) in adjacent load paths, run the WFD susceptibility screening, and flag when a supplemental inspection (for example the supplemental inspection document, SID/SLWFD) is required for fatigue critical baseline structure. Produces the MSD site-count verdict, the WFD susceptibility verdict, a...

Use when a fluctuating load case must be checked against a mean-stress fatigue limit or a Haigh diagram / fatigue diagram comparison is needed for a structure. Determine the allowable stress amplitude for infinite life under mean stress: compute the modified Goodman, Gerber, and Soderberg allowable amplitudes from the endurance limit, ultimate strength, and yield strength, plot the Haigh diagram with the design point, and give the infinite-life verdict when the applied amplitude exceeds the a...

Use when you must build a fatigue load spectrum from a mission load history: count cycles with the rainflow method, derive level-crossing and exceedance spectra, aggregate per-phase loads into a mission spectrum, apply spectrum truncation, and evaluate cumulative damage with Miner's rule on a Basquin S-N curve. Produces the rainflow cycle counts, the exceedance spectrum table, the truncated spectrum, and the cumulative damage fraction that gate the fatigue life assessment. Trigger: rainflow, ...

Use when you must evaluate fatigue life with cumulative damage: sum the Palmgren-Miner damage fractions over the load spectrum, check the total against the life limit, and report the percentage of fatigue life consumed. Produces the cumulative damage fraction, the life limit verdict, and the life consumed percentage that gate the fatigue assessment. Trigger: fatigue, cumulative damage, palmgren-miner, load spectrum, fatigue life, damage tolerance.

Use when a hole, fillet, or other stress raiser must be accounted for in a fatigue assessment of a structure. Compute the stress concentration factor and fatigue notch factor for a notched aerospace part: determine Kt for an elliptical or circular hole from the geometry, estimate the Peterson material constant from the ultimate tensile strength, convert Kt into the fatigue notch factor Kf with the Peterson and Neuber corrections using the notch root radius, evaluate the notch sensitivity q, a...

Use when you must estimate fatigue damage directly from a random-vibration response PSD: compute the psd-spectral-moments of a one-sided stress power spectral density by trapezoid integration, derive the expected-peak-rate, and apply the narrow-band Rayleigh model and the Dirlik amplitude mixture (dirlik-method) for the expected damage rate under a Basquin S-N curve with gamma closed forms; convert each damage rate to a fatigue life in hours. Produces the spectral moments, the expected peak r...

Use when you must determine the strain-life (low-cycle fatigue) endurance of an aerospace structure: Coffin-Manson total strain amplitude from reversals to failure, reversals to failure from a fully reversed strain amplitude, the transition life where elastic and plastic amplitudes cross, low-cycle versus high-cycle regime categorization, the Neuber local-strain rule that converts a nominal elastic stress at a notch into local elastic-plastic strain through the cyclic Ramberg-Osgood curve, an...

Use when S-N test data must be reduced to a Basquin curve, an endurance limit must be determined from runout tests, or a fatigue life must be predicted from a stress amplitude for a structure. Determine the stress-life (S-N) fatigue curve from test data and use it for fatigue life prediction: fit the Basquin equation S = A * N^b to the S-N test points by log-log regression, read the endurance limit from the runout stress level, and predict the cycles to failure at a given stress amplitude or ...

Use when you must margin-check a compression member that also carries bending: compute the Euler load P_E, the moment amplification factor delta that grows the moment as the axial load nears the Euler load, the amplified moment, the secant-formula peak compressive stress of an eccentrically loaded column, and the axial-plus-bending interaction ratio with its margin of safety and pass verdict. Produces P_E, the amplification factor, the amplified moment, the peak combined stress, the interacti...

Use when you must solve a two-dimensional rigid-jointed frame with the Euler Bernoulli beam element: build the local beam element stiffness from the axial and bending contributions, rotate it into the global frame with the member orientation, assemble the global stiffness matrix, apply the fixed support conditions, solve for the nodal displacements and rotations with a compact elimination solver, and recover the support reactions and the member end actions. Produces the nodal displacement and...

Use when you must compute the natural frequencies of a continuous beam member: exact Euler-Bernoulli bending frequencies in hertz for pinned-pinned, cantilever, clamped-clamped and free-free end conditions from the characteristic-equation roots cos x cosh x = -1 and cos x cosh x = 1, the closed-form pinned-pinned law n^2 pi^2 sqrt(EI/(m L^4))/2pi, the shared rule f_n = (beta_n L)^2 sqrt(EI/(m L^4))/2pi, and a Rayleigh-quotient fundamental estimate omega^2 = 20 EI/(m L^4) for non-uniform canti...

Use when a column, strut, spar cap, landing-gear leg or actuator rod must be sized or margin-checked against elastic instability in a stdlib-only environment without FEA software. Calculate the Euler critical buckling load of slender compression members: apply Pcr = pi^2*E*I/(K*L)^2 for pinned-pinned, fixed-fixed, fixed-pinned and cantilever end conditions, resolve the effective length factor K from the support type, compute the slenderness ratio from the radius of gyration, and run the buckl...

Use when running or checking linear static finite element analysis for aircraft structure with CalculiX (ccx): determine margin of safety from allowables versus FEA stresses, validate unit discipline before post-processing, and check von Mises stress results. The skill covers element-basis stress checks, margin computation, and unit conversion discipline so that allowables and computed stresses are compared in consistent units. Trigger: finite element, fea, calculix, ccx, stress analysis, mar...

Use when you must understand or verify a nonlinear finite element static analysis in the CalculiX (ccx) style: solve the equilibrium of a structure whose stiffness depends on its own state, apply Newton-Raphson iteration with load stepping, check convergence against a residual tolerance, and report the convergence verdict. The scalar model is a bar with state-dependent axial stiffness k(u) = k0 * (1 + alpha * u); the solver iterates u_{n+1} = u_n - r(u_n) / kt(u_n) with residual r(u) = k(u)*u...

Use when the task is FEA contact, penalty or Lagrange methods, contact stiffness, penetration, friction, stick-slip, master-slave contact, node-to-surface, or tied interfaces in bolted joints and bearing contacts. Compute finite element contact analysis quantities for aircraft structure: determine normal contact forces with the penalty method from contact stiffness and penetration, estimate penalty stiffness from the contacting element properties, check Lagrange multiplier enforcement of zero...

Use when you must compute the local crippling and inter-rivet allowables of a formed compression stiffener (angle, channel, Z, hat stringer, bulb angle): compute the element crippling stress F_cc = min(F_cy, C*sqrt(F_cy*E)*(t/b)**0.75) with the shape constants C = 0.31 for one-edge-free flanges and C = 0.55 for webs between corners, average the element crippling loads over the section area, compute the inter-rivet buckling stress of the attached flat from the rivet pitch, and run the Johnson-...

Use when you must stress-check a curved member with the Winkler curved-beam correction: compute the neutral-axis radius from the closed form A / integral(dA / rho) for a rectangular radial or circular tube section, take the neutral-axis-eccentricity, resolve the Winkler inner and outer fiber stresses, add the axial stress P / A, compare the inner fiber to the straight Euler-Bernoulli reading for the curved-beam amplification, and return the stress-to-allowable ratio with the pass or fail verd...

Use when you must compute the buckling of a curved unstiffened circular cylindrical shell with the NASA SP-8007 knockdown method: the axial-compression knockdown factor from the shell radius and thickness, the axial critical buckling stress 0.605*gamma*E*t/r, the bending knockdown factor, the bending critical moment, the cross-section ovalization collapse moment, and the plasticity correction factor. Produces the knockdown factors, the critical stress and moments, and the governing verdict be...

Use when you must analyze a plane shear web above its shear-buckling stress with the diagonal tension field idealization: compute the tension field ratio of the applied shear above the buckling stress, take the classical 45 degree tension field angle or accept the angle for a non-45 web, and compute the diagonal web tension stress, the flange and end post axial loads from the diagonal tension, the rivet shear flows on the flange and end post attachments, and the margin against buckling. Produ...

Use when you must compute the general Hertz elliptical contact patch between two elastic bodies with unequal principal radii pressed together: form the per-plane curvature sums A and B from the signed principal curvatures (convex positive, concave negative, flat infinite), solve the hertz-elliptic-integrals eccentricity from the unequal curvature ratio, then the contact-ellipse major and minor semi-axes a and b, the peak pressure p0 = 3P/(2 pi a b), the approach, the patch area and the yield-...

Use when you must compute the Hertzian contact stress between curved elastic bodies pressed together: determine the contact patch radius or half-width for sphere pairs, sphere-on-flat, ball-in-socket, cylinder pairs, cylinder-in-bore, roller-in-race or crossed cylinders from the load, the equivalent radius of curvature and the equivalent elastic modulus with 1/E* = (1-nu1^2)/E1 + (1-nu2^2)/E2; compute the maximum contact pressure p0 = 3P/(2 pi a^2) (circular) and p0 = 2P/(pi b L) (strip); rep...

Use when you must compute the inelastic column strength of a solid round, tube or extruded compression member in the intermediate slenderness band: the effective slenderness lambda = K*L/r of the member, the euler-johnson-tangent transition lambda_t = sqrt(2*pi^2*E/F_cy) where the yield-anchored Johnson parabola meets the Euler arm at F_cy/2, the johnson-parabola stress F_col = F_cy*(1 - F_cy*lambda^2/(4*pi^2*E)) below the transition and the Euler arm stress above it, the column capacity P_co...

Use when you must analyze a metallic pin-loaded lug fitting under an axial load: compute the hole bearing stress, the net section tension stress across the lug width, the tearout shear stress on the two planes from the hole tangent to the round outer contour, the per-mode margins against the material tension, shear and bearing allowables, the governing failure mode and the pass/fail verdict, the limiting allowable capacity, and the governing-mode map over the edge distance ratio for a round-e...

Use when you must analyze a metallic multi-fastener joint: split the applied load into the per-fastener share of a symmetric bolt or rivet pattern, check the fastener shear in single or double shear, the sheet bearing P/(D*t), net-section tension across the row and shear-out at the edge distance, and resolve an eccentric bolt group by the polar moment method for a load applied off the pattern centroid. Produces the per-fastener loads, the shear, bearing, net-section and shear-out stresses, th...

Use when you must run a modal analysis of a two degree of freedom mass-spring structural model: compute the natural frequencies in rad/s and Hz, derive the mode shape ratios, and check an excitation frequency against the natural frequencies for resonance risk. Units are SI: masses in kg, stiffnesses in N/m, frequencies in rad/s and Hz. Trigger: modal analysis, natural frequency, mode shape, resonance, eigenvalue, vibration, two degree of freedom.

Use when you must find the plastic collapse (limit) load of a beam or a simple frame: compute the fully plastic moment Mp = sigma_y*Zp from the plastic section modulus Zp (rectangle b*h^2/4, circle d^3/6, I-beam with the plastic neutral axis in the web), the shape factor nu = Zp/Z, and the plastic hinge mechanisms of statically indeterminate beams and rectangular frames, applying the kinematic (virtual work) and static (equilibrium plus yield) theorems to give the plastic collapse load, the c...

Use when a wing or fuselage skin panel, spar web or flat panel must be margin-checked against elastic instability in a stdlib-only environment without FEA software. Calculate the elastic buckling of flat plates and skin panels under compression and shear: resolve the plate buckling coefficient k from the edge conditions and the panel aspect ratio (k = 4.0 for a simply supported long plate, 6.97 for a clamped long plate), compute the critical compression buckling stress sigma_cr = k*pi^2*E/(12...

Use when you must size a fuselage pressure-bulkhead dome: compute the membrane stresses of a spherical cap, a hemisphere, or a 2:1 ellipsoid closing a pressurized cylindrical barrel with membrane theory, including the apex and equator meridional and circumferential stresses of an ellipsoidal dome, the dome margin against ultimate strength under the FAR 25.303 1.5 factor of safety, the spherical-cap rise, and the unbalanced meridional-resultant junction ring load at the dome-barrel interface w...

Use when you must compute the restrained (non-uniform) torsion response of a thin-walled open I-beam section: the warping constant Cw = I_y*h^2/4 of the doubly symmetric I-section, the sectorial coordinate at the flange tip, the decay parameter k = sqrt(G*J/(E*Cw)) of the non-uniform torsion equation E*Cw*theta'''' - G*J*theta'' = 0, the hyperbolic closed-form twist and twist rate, the bimoment B = -E*Cw*theta'' and the warping normal stress sigma_w = B*omega/Cw at the flange tip for a built-...

Use when you must locate the shear center of a thin-walled open section under transverse shear: walk the contour from the free edge accumulating the first moment Q, build the V*Q/I shear-flow distribution, integrate the wall-shear resultant and its moment, and report the shear-center offset from the web, centroid or corner in millimeters for channel, Z, angle, hat and slit single-cell box sections, with the bending shear-stress check tau = V*Q/(I*t) at the critical wall station. Doubly symmet...

Use when you must compute the shrink-fit contact pressure and stresses of a two-cylinder radial-interference assembly: convert the total radial interference into the interface contact pressure from the Lame thick-cylinder radial compliance of both members, recover the bore radial and hoop stresses at the critical bore of each member, form the von-Mises yield margin of each bore against its yield strength, and close with the governing member and the maximum allowable radial interference before...

Use when you must find the elastic end moments and support reactions of statically indeterminate beams and continuous beams: compute the fixed-end moments (uniform w*L^2/12 and central P*L/8 hogging at both fixed ends; w*L^2/8 and 3*P*L/16 hogging at the fixed end of a propped cantilever), solve the interior support moments with the three-moment (Clapeyron) equation, apply the moment distribution (Hardy-Cross) method with distribution factors and the 1/2 carry-over, and the slope-deflection a...

Use when you must compute the torsion shear flow of a closed or open structural section: the polar second moment J for solid and tube shafts, the Saint-Venant torsion constant for thin open rectangles and built-up open sections, the Bredt-Batho closed-section shear flow q = T/(2 A_m), the closed-section twist rate, the shear stress and torsional stress margin, and the multi-cell shear-flow distribution of a two-cell section under an applied torque. Produces the shear flow, twist rate, shear s...

Use when a truss model must be solved by hand or in a stdlib-only environment without FEA software. Compute the response of a 2D pin-jointed truss with the direct stiffness method: build each element stiffness matrix from E, A, L and orientation, assemble the global stiffness matrix, apply support conditions, solve the nodal displacements by Gaussian elimination, then recover member axial forces and support reactions. Units are SI. Trigger: truss analysis, direct stiffness method, element sti...

Use when you must compute the continuous turbulence gust design loads of an airplane by the power spectral density gust method: build the von Karman or Dryden power spectral density of the vertical gust velocity from the scale of turbulence and the turbulence intensity, form the rigid-aircraft gust response transfer function, multiply into the response power spectral density, integrate to the rms load response and scale to the design limit load factor of the continuous turbulence design crite...

Use when you must compute aircraft structural loads from gust and maneuver conditions per FAR 25.341 and FAR 25.337: discrete 1-cosine gust load factor n = 1 + (rho0*V_e*a*K_g*U_de)/(2*W/S), gust alleviation factor K_g = 0.88*mu_g/(5.3+mu_g) with mass ratio mu_g = 2*(W/S)/(rho*cbar*a*g), limit maneuvering load factor 2.5 (normal) or 3.8 (commuter/transport) at VA with linear variation to 0 at VD, V-n diagram construction with the corner point at VA and gust lines at VB/VC/VD, envelope verdict...

Use when you must compute the ground loads on an aircraft structure for the certification landing and ground-handling conditions: the static nose and main gear reactions from the weight and CG position over the wheelbase, the level-landing reactions at a limit vertical inertia load factor, the braked-roll deceleration and brake force from the main gear friction, the tail-down-condition reaction with the nose gear unloaded, and the one-wheel-load reaction from the lateral CG offset over the tr...

Use when you must compute the random vibration response of a structure or equipment item to a base-input acceleration power spectral density: single-degree-of-freedom transmissibility |H(f)|^2 = 1/((1-r^2)^2 + (2*zeta*r)^2), response PSD G_out(f) = |H(f)|^2 * G_in(f), RMS response in g from the Miles equation sigma = sqrt((pi/2)*f_n*Q*G_in(f_n)) with Q = 1/(2*zeta), numerical integration of the response PSD over a supplied spectrum, 3-sigma peak level, and the equivalent static load factor n_...

Use when you must compute the shock response spectrum (SRS) of a transient base acceleration pulse for shock qualification of equipment: single-degree-of-freedom oscillator peak response over a frequency grid at fixed damping, RK4 integration of the oscillator equation x_ddot + 2*zeta*wn*x_dot + wn^2*x = -a_base(t), half-sine pulse A*sin(pi*t/T) and decaying-sine pulse A*sin(2*pi*fd*t)*exp(-t/tau) support, peak pseudo acceleration wn^2 times peak relative displacement, the SRS curve as freque...

Use when you must compute the crack-tip-plasticity-correction for a crack in metallic structure: evaluate the Irwin plastic-zone radius in plane stress r_p = (1/pi)*(K/sigma_ys)^2 and the reduced plane-strain zone (1/(3*pi))*(K/sigma_ys)^2, form the effective-crack-length a_eff = a + r_p from the uncorrected elastic K, compute the corrected stress intensity K_eff = Y*sigma*sqrt(pi*a_eff), and judge the LEFM-validity verdict from the zone-to-crack ratio against the 2.5*(K/sigma_ys)^2 size rule...

Use when you must assess the elevated-temperature creep and stress rupture behavior of an aerospace metallic part: compute the steady-state creep strain rate with the Norton power law eps_dot = A * sigma^n * exp(-Q/(R*T)) from the stress and the temperature, estimate the rupture life in hours with the Larson-Miller parameter from the stress-LMP master curve, apply the Monkman-Grant relation between the minimum creep rate and the rupture life, accumulate the creep strain over the service time,...

Use when you must compute the stress relaxation of a preloaded metallic part held at fixed total strain at elevated temperature: evaluate the closed-form integral of the fixed-strain relaxation ODE for a Norton power-law creeping material, the relaxed stress sigma(t) = [sigma_0^(1-n) + (n-1)*A*E*t*exp(-Q/(R*T))]^(1/(1-n)) from the initial preload stress, the hold time, the temperature and the Norton constants A, n, Q and elastic modulus E, the retained-preload fraction after the hold, the tim...

Use when you must apply the plane-strain fracture toughness K_IC of an aerospace material: compute the applied stress intensity K = Y * sigma * sqrt(pi * a) for a crack of size a under remote stress sigma with geometry factor Y, check the failure criterion K >= K_IC, size the critical crack at which fast fracture starts, and judge whether a test specimen meets the ASTM E399 plane-strain validity requirement that thickness and crack size both exceed 2.5 * (K_IC / sigma_ys)^2. Connects fracture...

Use when you must select a structural material for an aerospace component: compare candidate materials across the aluminum, titanium, steel, and composite families, compute Ashby-style selection indices (E/rho for tension stiffness, E^(1/2)/rho for beam bending, E^(1/3)/rho for panel bending, sigma/rho for strength-limited tension), and rank candidates by stiffness-to-weight and strength-to-weight. Covers design drivers: temperature limits, corrosion and galvanic coupling, cost and availabili...

Use when computing statistically based metallic material design allowables per MMPDS: determine A-basis and B-basis values from coupon test data, run the one-sided normal tolerance k-factor approximation, and validate that derived allowables sit below the sample mean. The skill applies minimum sample counts, confidence/content conventions, and sanity checks on design values, following the statistical approach of MMPDS and its MIL-HDBK-5 heritage. Trigger: allowables, a-basis, b-basis, k-facto...