Composite Material and Structure

Irreversible deformation theory essential for engineering design and material analysis.The formula is given by: Where: σ is the stress tensor, ϵ is the strain tensor, ϵp​ is the plastic strain tensor, f is a function describing the material’s yield behavior.

Measures adhesive’s ability to withstand applied forces between materials. The formula is given by: Where: Bond Strength is the adhesive bond strength, Force is the maximum force required to pull apart the bonded materials, Area is the bonded area between the materials.

Hertzian contact stress is an Analyzes stress between elastic bodies.The formula is given by: Where: σ is the Hertzian contact stress, F is the normal force applied to the contact area, R1​ and R2​ are the radii of curvature of the contacting surfaces.

Analyzes rotor stability, plots natural frequencies against rotational speed.The formula is given by: Where: Ω is the rotational speed of the structure (in radians per second), ωn​ is the natural frequency of the composite structure (in radians per second).

Describes mass distribution and dynamic response in structural analysis.The formula is given by: Where: M is the mass matrix, a is the acceleration vector, f is the force vector.

Describes stiffness properties, force-displacement relationship, crucial in structural analysis.The formula is given by: Where: K is the stiffness matrix, u is the displacement vector, f is the force vector.

Describes structure’s response to harmonic excitation across frequencies.The formula is given by: Where: H(ω) is the Frequency Response Function, X(ω) is the complex amplitude of the response at frequency ω, F(ω) is the complex amplitude of the input excitation at frequency ω.

Rayleigh damping is a Linear model combining mass and stiffness matrices.The formula is given by: Where: C is the damping matrix, α and β are the Rayleigh damping coefficients, M is the mass matrix, K is the stiffness matrix.

Dynamic analysis studies system behavior under varying loads over time.The formula is given by: Where: F is the force acting on the system, m is the mass of the system, and a is the acceleration of the system.

Identifies, assesses, prioritizes potential failure modes and effects.The formula is given by: Where: Severity: Refers to the potential impact or seriousness of the failure mode on system performance. Occurrence: Indicates the likelihood or frequency of the failure mode occurring. Detection: Represents the effectiveness of existing detection methods in identifying the failure mode before it causes harm.