Bolted and hybrid composite joints
These separate mechanical studies use the linked laminate for thickness and specially orthotropic extensional stiffness. Strengths, retained pretension, connector stiffness and through-thickness modulus are explicit inputs with a recorded parameter basis.
Pretension, slip and failure onset
Washer pressure is closing force divided by annular area; thickness strain is minus pressure divided by Ez. The same closing force passes through both washers. Faying friction is an elastic stick law capped by μ times retained closing force times the number of active interfaces. Bearing engages after radial clearance is taken up. The model estimates first nominal failure from independently supplied bearing, net tension, shear-out, bolt shear and clamp compression strengths.
Finite-difference fields
The CDS membrane discretization minimizes strain energy using first-order finite differences of displacement and the laminate A matrix. Free coupon edges, tensile and bypass tractions, a unilateral radial pin spring and a prescribed washer-footprint friction load define equilibrium. The solver reports residual and force balance. Local stresses are membrane averages; uniform washer σz/εz are superposed estimates. It does not resolve washer-edge interlaminar stresses, depthwise pressure spreading, ply damage, countersinks or single-lap bending. Compare grids and averaged stresses before interpreting peaks.
Hybrid bonded/bolted lap
Two equal axial adherends exchange shear through the adhesive and discrete fasteners. Relative displacement obeys δ″ = 2kδ/(EA) between bolts, with force jumps at each connector. The analytical Green-function and conservative finite-difference alternatives solve the same elastic/Coulomb/clearance connector law. Adhesive transfer plus fastener transfer equals applied force. Bolting and bonding capacities are not simply added. The separate Goland–Reissner bonded-only model remains useful for eccentricity comparison; hybrid peel is not computed here.
Exercises and test references
D5961 organizes bearing-response experiments. D7248 uses two fasteners to investigate bearing/bypass interaction. D7332 addresses fastener pull-through, and D6873 addresses bearing fatigue; those latter mechanisms are not solved by this static membrane model. All supplied sizes are editable original teaching choices. These exercises do not reproduce the standards or establish compliance, allowables or certified ultimate strength.