Composite Material and Structure

Numeric technique for solving differential equations in engineering.The formula is given by: Where: K is the global stiffness matrix of the system, U is the vector of unknown displacements, F is the vector of external forces applied to the system.

Curvature equals moment divided by flexural rigidity.The formula is given by: Where: κ is the curvature of the structural member, M is the bending moment applied to the member, E is the modulus of elasticity (Young’s modulus) of the material, I is the moment of inertia of the cross-sectional area of the member about the axis of bending.

Shear modulus calculated from Young’s modulus and Poisson’s ratio.The formula is given by: Where: E is Young’s modulus, which represents the stiffness of a material in the linear elastic region. ν is Poisson’s ratio, which describes the ratio of transverse contraction strain to longitudinal extension strain in the direction of stretching force.

Lamé’s first parameter relates the material’s elastic properties to its bulk modulus and shear modulus.The formula is given by: Where: E is the Young’s modulus of the material. ν is Poisson’s ratio.

Traction equals fracture toughness times separation in fracture mechanics.The formula is given by: Where: T is the traction (stress) along the crack or interface. d is the separation (displacement) between the crack surfaces. K is the slope of the Traction Separation Law curve, often referred to as the “fracture toughness” or “critical energy release rate”.

Length divided by radius of gyration determines slenderness ratio.The formula is given by: Where: L is the length of the column. r is the radius of gyration.

Effective stress formula for shear lag analysis in structures.The formula is given by: Where: σeff​ is the effective stress at a distance y from the fastener row. T is the applied tensile force. A is the cross-sectional area of the plate. g is the distance between fasteners.

Bolted joint analysis involves stiffness, preload, and external loads.The formula is given by: Where: K is the stiffness of the joint. Fmax​ is the maximum axial force the joint can withstand before failure. Fmin​ is the minimum axial force to maintain joint contact. d is the axial displacement of the joint due to the external load.

Wagner’s theorem predicts composite material stiffness distribution in laminates.The formula is given by: Where: Ec​ is the effective modulus of elasticity of the composite. Vf​ is the volume fraction of the fiber (or reinforcing phase). Ef​ is the modulus of elasticity of the fiber. Vm​ is the volume fraction of the matrix. Em​ is the modulus

Lamé’s equation predicts composite material deformation under applied stress.The formula is given by: Where: σ is the stress tensor ε₁, ε₂, ε₃ are the principal strains λ and μ are Lamé’s first and second parameters, respectively, which are material constants.