Application and Implementation of Finite Element Methods by J. E. Akin

By J. E. Akin

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The specific input instructions are presented in Appendix A. Later applications will illustrate the use of these properties. In some applications, the initial forcing vector (system column matrix) terms will be known to be non-zero. In such cases, the non-zero initial contributions must be input by the analyst. Subroutine INVECT reads these contributions and then prints the entire initial load vector. The subroutine is also shown in the Appendix, as are the corresponding input instructions. In subroutine INVECT each specified coefficient has an identifying parameter number and system node number associated with it.

Once the number and type of nodal parameter boundary conditions have been determined, it is necessary to supply the constraint equation data. These nodal parameter constraint data are read by subroutine INCEQ (see Appendix). 1. 1) TYPE3 ADJ+BDk+CDI=E where A, B, C, and E are constants and j, k, and I denote system degree of freedom numbers associated with the nodal parameters (D). The program can easily be expanded to allow for nine types of linear constraint equations. Regardless of which type of constraint equation one has, it is still necessary for the analyst to input the constant(s) and identify the degree of freedom number(s).

The system equations usually occupy a very large percentage of the total storage. Knowing the system equation's half-bandwidth, determined above, and the total numbers of 37 3. Pre-element calculations 38 degrees of freedom in the system, the storage requirements for these banded, symmetric equations are easily determined. It is possible for nodal parameter constraint equations to increase the half-bandwidth of the system equations. This depends on how the constraints are implemented. There are certain basic operations that must be carried out before one actually generates the element matrices for the particular problem under study.

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