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With the mathematical model chosen, finite element procedures are used to solve the model.
Using the traditional finite element procedures necessitates using thousands of elements and nodal points.
The analysis starts from a fundamental virtual work equation and uses standard finite element procedures.
Classical finite element procedures are not well suited to the development of optimal acoustical shapes.
From the advent of free (open) boundary conditions, they were confined to mixed finite element procedures.
In this study, finite element procedures for the ultrasonic welding process are developed using 2D plain-strain elements.
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Carnicero and Lopez-Garcia [37] adopt the nonlinear finite element procedure to establish the catenary model.
For these purposes, a nonlinear finite element procedure is applied using pressure eigenforms as equivalent loads.
A consolidated single S N curve is obtained based on a systematic finite element procedure.
The matrix notation is used in formulating and solving problems using the finite element procedure.
The system of nonlinear finite element equations is derived based on the finite element procedure.
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