Package for Machine Design

Finite Element Analysis in Structural Mechanics

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en:ref:name:id

Table of Contents

name.iD

HMOD

Format

; program control IP KOUT KDUMP KPRIN KKIN RP TEND DT

; description of integer/real vectors of arbitrary length VC IB T 1 I/R $\dots$ I/R $\dots$

; basic temporal description of excitation RS IB T 1 I NFOUR NPOL

; assignment of meaning to the vectors defined by a VC-batch or read from file AS IB T 1 I ISET KFEAT I IDISC IREC KFEAT I $\dots$

; end of input data EN EN

Annotations

$\mathtt{KOUT}$The key of output to the protocol.
$=0$no output (can be used to check the input data)
$=1$components of nodal displacements
$=2$components of nodal displacements and velocities
$=3$components of nodal displacements, velocities and accelerations
$\mathtt{KDUMP}$The key of output to the binary file name.S.
$=0$no output
$=1$output the displacement field after each time step
$=2$output the displacement field in selected time steps
$\mathtt{KPRIN}$The key of printing the header to the protocol.
$=0$no header
$=3$print header
$\mathtt{KKIN}$The key of excitation.
$=0$force excitation (prescribed displacement conditions are time-independent)
$=1$harmonic kinematic excitation
$=2$seismicity
$\mathtt{TEND}$The time to be reached at the end of the computation $[\text{s}].$
$\mathtt{DT}$The integration step $[\text{s}]$ for integration of the right-hand side which is assumed to be piecewise linear in time. The times for output of the quantities are rounded to integer multiples of $\mathtt{DT}.$
$\mathtt{IB}$The batch number.
$\mathtt{NFOUR}$The number of terms of the Fourier series, $\mathtt{NFOUR}\le100.$
$\mathtt{NPOL}$The order of the polynomial of the Fourier series, $\mathtt{NPOL}\le35.$
$\mathtt{ISET}$The index at which the vector is specified in the VC batch.
$\mathtt{KFEAT}$The key specifying the physical meaning of the quantity described by the vector.
$\mathtt{IDISC}$The number of the file from which the vector is read.
$=1$name.1
$=2$name.2
$\mathtt{IREC}$The number of the record in the binary file $\mathtt{IDISC}.$
$\mathtt{KFEAT}$ Key letter Vector length Physical meaning of the quantity (see notes below)
1 R $\mathtt{LSOL}$ components of nodal displacements; $\mathtt{LSOL}$ is the number of degrees of freedom of the mesh
2 R $\mathtt{LSOL}$ components of nodal velocities
3 R $\mathtt{LSOL}$ $\mathbf{R}_0$ or $\mathbf{u}_0$ (according to $\mathtt{KKIN}$)
4 R $\mathtt{NFOUR}$ $A_1,A_2,\dots,A_\mathtt{NFOUR}$
5 R $\mathtt{NFOUR}$ $B_1,B_2,\dots,B_\mathtt{NFOUR}$
6 R $\mathtt{NFOUR}$ $\omega_1,\omega_2,\dots,\omega_\mathtt{NFOUR}$
7 R $\mathtt{NPOL}+1$ $a,C_1,C_2,\dots,C_\mathtt{NPOL}$
8 R $\mathtt{NROOT}$ $\xi_1,\xi_2,\dots,\xi_\mathtt{NROOT}$; $\xi_k$ are the parameters of modal damping and $\mathtt{NROOT}$ is the number of calculated eigenpairs; for each node of the damped structure it holds $\omega_\text{damped}^2=\omega^2(1-\xi^2)$
9 R $\le50$ times $t_{d1},t_{d2},\dots~[\text{s}]$ for the dump and output to the protocol (mandatory for $\mathtt{KDUMP}=2$)
10 I $\le\mathtt{NNOD}$ the list of node numbers for the output to the protocol (not affected by $\mathtt{KDUMP}$); $\mathtt{NNOD}$ is the number of nodes in the mesh
11 R $\le50$
(even number)
times $t_{L1},t_{U1},t_{L2},t_{U2},\dots~[\text{s}]$ defining the intervals $(t_{Li},t_{Ui}),$ where $f(t-t_{Ui})=f(t)\equiv0$
12 R $3\cdot\mathtt{NROOT}$ $(a_1,\dots,a_\mathtt{NROOT})_x,$ $(a_1,\dots,a_\mathtt{NROOT})_y,$ $(a_1,\dots,a_\mathtt{NROOT})_z$; $a_i$ are acceleration components in the direction of global axes $x,y,z$ for $\mathtt{NROOT}$ calculated eigenvectors

The information in the RS batch, together with the information in the VC batch, specify the time characteristics of the excitation. The excitation $\mathbf{b}(t)$ is assumed in the form of a product (skleronomic) vector $\mathbf{b}_0$ and a scalar function of time $f(t),$ i.e., $$\mathbf{b}(t) = \mathbf{b}_0f(t).$$ The vector $\mathbf{b}_0$ contains axial components of amplitudes, either

  • nodal forces $\mathbf{R}$ in all nodes of the mesh $\mathbf{R}_0=\mathbf{b}_0$ for $\mathtt{KKIN}=0,$ or
  • nodal displacements $\mathbf{u}$ in all nodes of the mesh $\mathbf{u}_0=\mathbf{b}_0$ for $\mathtt{KKIN}=1.$

The time function $f(t)$ is designed in the form of product of the partial sum of the Fourier series and a polynomial, i.e., \begin{align} f(t) &= F(t)P(t),\\ F(t) &= \sum_{k=1}^\mathtt{NFOUR}\left[A_k\cos(\omega_kt)+B_k\sin(\omega_kt)\right],\\ P(t) &= e^{at}\left(C_1t^{\mathtt{NPOL}-1}+C_2t^{\mathtt{NPOL}-2}+\dots+C_{\mathtt{NPOL}-1}t+C_\mathtt{NPOL}\right). \end{align}

Note
$\mathtt{NFOUR}=0$ implicates $F(t)=1,$ $\mathtt{NPOL}=0$ implicates $P(t)=1.$
Note
If the excitation acts only on a few nodes, it is convenient to use the condensed notation for $\mathbf{b}_0.$
If the excitation is distributed to many nodes, or if it is a subject of calculation or measurement, it may be advantageous to provide $\mathbf{b}_0$ in the special file name.1 (or name.2).
Note for $\mathtt{KFEAT}=3$
The zero force component in $\mathbf{R}_0=\mathbf{b}_0$ means that the excitation in that place and direction is zero. The zero displacement component in $\mathbf{u}_0=\mathbf{b}_0$ means the absence of kinematic excitation in that place and direction; in no way does it represent a > prescribed zero displacement.
Note for $\mathtt{KFEAT}=11$
The intervals $(t_{Li},t_{Ui}),$ $i=1,2,\dots,$ defined by the even number of ascending time levels $t_{L1},$ $t_{U1},$ $t_{L2},$ $t_{U2},\dots~[\text{s}]$ let the continuous-in-time excitation $\mathbf{b}(t)$ not be activated in intervals $(t_{Li},t_{Ui}),$ $i=1,2,\dots.$ As soon as the time $t$ reaches the value $t=t_{Ui},$ the program sets $t_0=t_{Ui}$ and for the next interval $(t_{Ui},t_{Li+1})$ it holds the excitement again as $$\mathbf{b}(t) = \mathbf{b}_0f(t-t_{Ui}) = \mathbf{b}_0f(t-t_0) = \mathbf{b}_0(t)f(t).$$
Note
For $\mathtt{KKIN}=0/1$ and $\mathtt{KDUMP}>0$ the binary file name.S is generated which contains for all ($\mathtt{KDUMP}=1$) or selected only ($\mathtt{KDUMP}=2$) time levels (which are integer multiples of the integration step $\mathtt{DT}$) two records: the first contains nodal displacements (of length $\mathtt{LSOL}$) and the second contains the time (of length $1$). This file has the same structure as the file name.FRQ generated by the program HFRQ, or the file name.S generated by the programs HNEW or STAB.
Note
For $\mathtt{KKIN}=2$ and $\mathtt{KDUMP}>0$ the binary file name.S is generated with two records: the first contains nodal displacements (of length $\mathtt{LSOL}$), the second contains nodal reactions supplemented by three numbers (of length $\mathtt{LSOL}+3$). This file has the same structure as the file name.SOL generated by the program FEFS in case of only one load case.
en/ref/name/id.txt · Last modified: 2024-11-27 15:18 by Petr Pařík