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Finite Element Analysis in Structural Mechanics

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en:user:problem:new:start

Transient response

Computation diagram

Computation steps

1. Prepare the computation

The solution of this problem must be preceded by the calculation of element stiffness matrices, and the following conditions apply:

The right-hand side (the load case) does not matter in this case; therefore, only quantities specifying material properties and displacement boundary conditions can be considered in the first load case (AS 1) in the name.i2 file.

Program RMD2, RPD2, SRH2 (2D problem) / RMD3, RPD3, SRH3 (3D problem)
Inputs name.i1, name.i2, name.i3
Report name.o1, name.o2, name.o3
Outputs binary files
Details Linear elastostatics, Computation overview / Reference Manual: Inputs

2. Calculate the mass matrices

The input data is written into the name.iM text file. The program generates consistent (thus positive definite) mass matrices $\mathbf{M}$ of elements.

Program HMOT (2D / 3D problem)
Inputs name.iM, binary files from the previous steps
Report name.oM
Outputs binary files
Details Computation overview / Reference Manual: Inputs

3. Calculate the damping matrices

The input data is written into the name.iC text file. The program generates Rayleigh proportional damping matrices $\mathbf{C}$ of elements. Regarding the definiteness of the generated matrices, nothing can be stated in advance.

Program HCRE (2D / 3D problem)
Inputs name.iC, binary files from the previous steps
Report name.oC
Outputs binary files
Details Computation overview / Reference Manual: Inputs
Note
Other types of damping matrices may also be considered; however, in such a case, the user must ensure they are stored in the name.AMP binary file and the HCRE program is not invoked.

4. Factorize the global matrix

The input data is written into the name.iR text file. The program factorizes the matrix $$\sum(\mathbf{K}+a_0\mathbf{M}+a_1\mathbf{C}),$$ where $\sum(\dots)$ denotes global (not element) matrices. The consistent mass matrix $\sum(\mathbf{M})$ is positive-definite, and the matrix $\sum(a_0\mathbf{M}+a_1\mathbf{C})$ usually exhibits the same property. Since quasi-static processes are not considered here, the matrix $\sum(\mathbf{K}+a_0\mathbf{M}+a_1\mathbf{C})$ will then also be positive-definite, even if $\sum(\mathbf{K})$ is only positive-semidefinite. It is recommended to check that no pivots smaller than $\mathtt{PIVOT}$ are reported in the name.oR file.

Program HFRO (2D / 3D problem)
Inputs name.iR, binary files from the previous steps
Report name.oR
Outputs binary files
Details Computation overview / Reference Manual: Inputs

5. Integrate the equations of motion

The input data is written into the name.iW text file. The solution algorithm is based on the Newmark direct integration method. General means are available for specifying the initial conditions, as well as force or kinematic excitation. Furthermore, the output control allows keeping the amount of result data within reasonable limits and facilitates subsequent graphical post-processing. The method may be used for both damped and undamped processes.

Program HNEW (2D / 3D problem)
Inputs name.iW, binary files from the previous steps
Report name.oW
Outputs binary files (the solution is in the name.S file)
Details Computation overview / Reference Manual: Inputs

6. Calculate the strains and stresses

The input data is written into the name.i5 text file, where the problem type key $\mathtt{KPROB}=1$.

Program STR2 (2D problem) / STR3 (3D problem)
Inputs name.i5, binary files from the previous steps
Report name.o5
Outputs name.STR (optionally), name.STB (optionally)
Details Computation overview / Reference Manual: Inputs
en/user/problem/new/start.txt · Last modified: by Petr Pařík