Composite Material and Structure

Calculate composite tensile strength using constituent strengths and volume fractions.The formula is given by: Where: σc​ is the tensile strength of the composite material. σm​ is the tensile strength of the matrix material. σf​ is the tensile strength of the reinforcement (fiber or filler) material. Vm​ is the volume fraction of the matrix material. Vf​ is […]

Composite formula describing stress-strain relationship in plastic deformation materials. The formula is given by: Where: σ is the stress, ε is the strain, E is the modulus of elasticity, εc​ is the strain at failure.

Nusselt number is a ratio of convective to conductive heat transfer.The formula is given by: Where: Nu is the Nusselt number h is the convective heat transfer coefficient L is a characteristic length scale (e.g., diameter for a pipe, length for a plate) k is the thermal conductivity of the fluid  

Relationship between applied force and deformation in material testing.The formula is given by: Where: σ is stress (force per unit area), ε is strain (change in length per unit length), E is the Young’s modulus (modulus of elasticity), which represents the stiffness of the material.

Shear force equals negative derivative of bending moment.The formula is given by: Where: V is the shear force at the point, M is the bending moment at the point, and dx is the infinitesimal length along the beam.

Beam deflection is a equilibrium between bending moment, material properties, and geometry.The formula is given by: Where: δ is the deflection at the center of the beam P is the applied load L is the length of the beam E is the modulus of elasticity of the beam material I is the second moment of area

Plate deflection is a bending stress and applied loads equilibrium equation.The formula is given by: Where: w is the maximum deflection at the center of the plate. q is the uniform load acting on the plate. a is the length of one side of the plate. D is the flexural rigidity of the plate, which is

Shell deflection is a balance between curvature and applied loads.The formula is given by: Where: δ is the deflection, p is the applied pressure, r is the radius of the shell, E is the modulus of elasticity of the shell material, t is the thickness of the shell.

Frequency (f) equals one over the period (T).The formula is given by: Where : T is the period of the wave, the time it takes for one complete cycle.

Damping ratio equals damping coefficient divided by critical damping value.The formula is given by: Where: c is the damping coefficient, m is the mass of the system, and k is the spring constant.