COMPUTATIONAL WELDING MECHANICS

Spatial Integration Schemes

Since the Finite Element Method (FEM) is primarily an exercise in numerical integration, it is not surprising that better integration schemes are being sought. Numerical integration schemes replace an

integral by a summation; e. g. J f(x)dx - ]T"=1 wif(xi). The choice

of the number of sampling points, i, the weights, wt, and the location of the sampling points, xh characterize the integration scheme. If f(x) is a polynomial of degree 2n-l, it can be integrated exactly with n sampling or integration points as shown by Gauss. In two dimensions, the stiffness matrix of the popular 4 node rectangular element (but not a quadrilateral) can be integrated exactly with four integration points. If only one integration point is used, the integration is approximate and spurious nodes may appear that corrupt the solution. Belytschko [16] discovered a way to stabilize these spurious nodes and thus reduce the integration costs by almost a factor of four for 4-node quads and almost 8 for 8-node bricks.

COMPUTATIONAL WELDING MECHANICS

Fracture Mechanics of Welded Structures

For fracture mechanics the location and geometry of the crack or defect must be specified as input data. The crack geometry could be specified as an ordered set of points …

Material Properties Summary

Properties can be provided for a material or alloy or for a specific phase in a material or alloy. If properties are provided for a specific phase, then the macroscopic …

Weld Pool Solver

If there is a weld pool solver that computes the weld pool free surface, velocity and temperature in the weld pool and weld pool reinforcement, the input data should include …

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