Random response for ply stress components

Power spectral density function of the ply stress response is expressed as:

S(ω)=\sum_{j=1}^{n}\sum_{k=1}^{n}ϕ_{yj}ϕ_{yk}Γ_{jx}Γ_{kx}{h^*}{j}(ω)h{k}(ω)S_{b}(ω)				where:ϕ_{yj} is the eigenvector j for the stress component y.ϕ_{yk} is the eigenvector k for the stress component y.Γ_{jx} is the modal participation factor for mode j along the excitation direction. Γ_{kx} is the modal participation factor for mode k along the excitation direction. {h^*}{j}(ω) is the complex conjugate of the transfer function for mode j. h{k}(ω) is the transfer function for mode k. S_{b}(ω) is the input enforced acceleration PSDF at the boundary node.

The variance of the response for the ply stress component y is calculated as:

(σ_{y}^{d}){x}^{2}=\int{ω_L}^{ω_J}S(ω)dω

The RMS stress is defined as:

RMS=\sqrt{(σ_{y}^{d}){x}^{2}}=(σ{y}^{d})_{x}

Random response for ply stress components, Simcenter 3D 2021.1 Series

© 2020 Siemens

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