Automated quadrilateral surface discretization method and apparatus usable to generate mesh in a finite element analysis system

In a finite element analysis method comprising generating a mesh of quadrilateral elements defining a geometric region to be analyzed, introducing a stimulus responsive to an input by an operator to which the response of the geometric region is to be modeled, performing finite element analysis on the geometric region in response to the stimulus to produce analysis data, and using the resulting analysis data, a method of automatically generating a mesh of quadrilateral elements comprising the steps of:

• inputting a permanent boundary on the exterior of the geometric region;
• and
• iteratively layering rows of quadrilateral elements inward from said permanent boundary to the interior of the geometric region to form the mesh of the quadrilateral elements defining the geometric region, said step of iteratively layering including the steps of,
• defining a plurality of fixed nodes along said permanent boundary,
• generating a paving row including the layered rows of quadrilateral elements around the inside of said boundary,
• smoothing said paving row of said boundary,
• seaming said paving row of said boundary,
• detecting when said paving row intersects itself or when said paving row intersects an existing portion of said mesh and connecting the intersecting portions,
• determining whether said paving row includes contracting or expanding quadrilateral elements and adjusting said paving row by inserting wedges or forming tucks,
• determining when six or less nodes remain in said paving row and completing said paving row by forming a seam or adding additional quadrilateral elements when six or less nodes remain, and
• inserting or deleting elements to improve local aspect ratios, reduce the number of irregular nodes and eliminate elements having interior angles less than a predetermined value to complete said paving row.

A method of automatically surface discretizing a geometric region into a plurality of quadrilateral elements, comprising the steps of:

• (a) inputting a permanent boundary on the exterior of the geometric region;
• and
• (b) iteratively layering rows of quadrilateral elements inward from said permanent boundary to the interior of the geometric region to form a mesh of the quadrilateral elements defining the geometric region, said step (b) including the steps of,
• (b)(1) defining a plurality of fixed nodes along said permanent boundary,
• (b)(2) generating a paving row including the layered rows of quadrilateral elements around the inside of said boundary,
• (b)(3) smoothing said paving row of said boundary,
• (b)(4) seaming said paving row of said boundary,
• (b)(5) detecting when said paving row intersects itself or when said paving row intersects an existing portion of said mesh and connecting the intersecting portions,
• (b)(6) determining whether said paving row includes contracting or expanding quadrilateral elements and adjusting said paving row by inserting wedges or forming tucks,
• (b)(7) determining when six or less nodes remain in said paving row and completing said paving row by forming a seam or adding additional quadrilateral elements when six or less nodes, and
• (b)(8) inserting or deleting elements to improve local aspect ratios, reduce the number of irregular nodes and eliminate elements having interior angles less than a predetermined value to complete said paving row.