Skyline Method

The skyline method solves the K * x = b linear equation system, or the eigenvalue problems Kφ - λB φ = 0 equation system.

The skyline method is based on the Cuthill-McKee reordering method ¹², a matrix profile scheme, and the Crout factorization technique ³.

This method is applied when solving either a linearized equation set or an eigenvalue problem Kφ - λBφ = 0 (modal and buckling analysis). If the second matrix B is consistent (modal analysis with consistent mass matrix or buckling), then it is stored by means of the profile method (as is the K matrix). All required consistent matrices for different types of analyses are also stored by means of the profile method. For example, a stress-stiffened matrix for nonlinear and buckling analysis and a dynamic matrix K - λB for Sturm sequence check and harmonic analysis.

Specifications

• Memory use: low
• Disk use: high
• Speed estimation: slow
• Quantity of equations: up to 50000 equations.
• Supported analyses: All.
• Available analysis limitations: N/A
• Additional remarks:The Skyline method often allows you to obtain numbers of nodes and degrees of freedom for equations leading to calculation problems such as incorrectly restricted structures.

Skyline Method calculations

The calculations dialog for the Skyline method shows the following phases:

• • Model reduction (renumbering of nodes and elements)
  • Definition of the stiffness matrix for individual structure elements
  • Matrix decomposition (Cholesky decomposition)
  • Number of blocks.
  • Division of the stiffness matrix. A part of the matrix is saved on the disk, slowing calculations.
  • Problem solving for successive load cases.