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김경종
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# Appendix III
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# Instructions for preparing input data for dynamic transient problems
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The program DYNPAK has been described in Section 10.6 and MIXDYN in Section 11.5. These programs perform large displacement or viscoplastic or elasto-plastic, transient dynamic analysis of plane stress/strain or axisymmetric problems respectively. The format of the input data is identical for both programs. In this appendix user instructions for preparing input data are provided.
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CARD SET 1 DYNAMIC DIMENSIONING (4I5)—One card.
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Cols. 1-5 NPOIN Total number of nodal points.
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6-10 NELEM Total number of elements.
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11-15 NDOFN Number of degrees of freedom per node $(= 2)$ .
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16-20 NMATS Number of different material sets.
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CARD SET 2 TITLE CARD (10A4)—One card.
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Cols. 1–40 Title of the problem—limited to 40 alphanumeric characters.
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CARD SET 3 CONTROL CARD (13I5)—One card.
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Cols. 1–5 NVFIX Total number of nodal points with fixed degrees of freedom.
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$$
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\begin{array}{l} = 1, \text { Plane stress }, \\ = 2, \text { Plane strain }, \\ = 3, \text { Axisymmetric problem. } \\ \end{array}
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$$
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6-10 NTYPE Type of problem:
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11-15 NNODE Number of nodes per element.
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16-20 NPROP Number of material properties $(= 11)$ .
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21-25 NGAUS Integration rule for stiffness matrix.
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26-30 NDIME Number of coordinate dimensions (=2).
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31-35 NSTRE Number of stress components (= 3 for plane stress/strain, = 4 for axisymmetric).
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<!-- source-page: 532 -->
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<table><tr><td>36-40</td><td>NCRIT</td><td>Yield criterion: = 1 — Tresca, = 2 — Von Mises, = 3 — Mohr-Coulomb, = 4 — Drucker-Prager.</td></tr><tr><td>41-45</td><td>NPREV</td><td>Indicator for the previous state to be read (= 1 for previous state, otherwise, = 0).</td></tr><tr><td>46-50</td><td>NCONM</td><td>Number of concentrated masses (≥1 if concentrated mass present, otherwise, = 0).</td></tr><tr><td>51-55</td><td>NLAPS</td><td>Indicator for large displacement analysis: = 0—Elastic analysis, = 1—Elasto-plastic small displacement analysis, = 2—Elastic large displacement analysis,</td></tr><tr><td>56-60</td><td>NGAUM</td><td>Integration rule for mass matrix.</td></tr><tr><td>61-65</td><td>NRADS</td><td>= 0, Read (r, z) coordinates for nodes, = 1, Read (R, Θ) coordinates for nodes for axisymmetric analysis.</td></tr></table>
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CARD SET 4 ELEMENT CARDS (11I5)—One card for each element, total of NELEM cards. The node numbers are read in anticlockwise sequence. The number of nodes depends upon the type of element. For four and eight noded elements read only four and eight nodes respectively.
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<table><tr><td>Cols.</td><td>1-5</td><td>IELEM</td><td>Element number.</td></tr><tr><td></td><td>6-10</td><td>MATNO</td><td>Material identification number.</td></tr><tr><td></td><td>11-15</td><td>LNODS(IELEM,1)</td><td></td></tr><tr><td></td><td>16-20</td><td>LNODS(IELEM,2)</td><td></td></tr><tr><td></td><td>21-25</td><td>LNODS(IELEM,3)</td><td></td></tr><tr><td></td><td>26-30</td><td>LNODS(IELEM,4)</td><td></td></tr><tr><td></td><td>31-35</td><td>LNODS(IELEM,5)</td><td>Nodal connection numbers.</td></tr><tr><td></td><td>36-40</td><td>LNODS(IELEM,6)</td><td></td></tr><tr><td></td><td>41-45</td><td>LNODS(IELEM,7)</td><td></td></tr><tr><td></td><td>46-50</td><td>LNODS(IELEM,8)</td><td></td></tr><tr><td></td><td>51-55</td><td>LNODS(IELEM,9)</td><td></td></tr></table>
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CARD SET 5 NODAL COORDINATE CARDS (I5,2F10.5)—One card for each node. Last nodal point (IPOIN=NPOIN) must be read at the end. Only corner and central nodes need to be specified. Midside nodes are interpolated if not specified. For axisymmetric cases, $(R, \Theta)$ values are read for NRADS = 1, and $(r, z)$ coordinates are calculated in the program.
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<!-- source-page: 533 -->
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Cols. 1-5 IPOIN Current nodal point.
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6-15 COORD(IPOIN,1) x-coordinate.\*
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16-25 COORD(IPOIN,2) y-coordinate.
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CARD SET 6 RESTRAINED NODE CARDS (1X,14,3X,211)—One card for each restrained node. Total of NVFIX cards.
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Cols. 2-5 IPOIN Restrained node number.
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9 IFPRE(IVFIX,1) Fixity in $x$ -direction $(= 0$ , Free; $= 1$ , Fixed).
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10 IFPRE(IVFIX,2) Fixity in y-direction (= 0, Free; = 1, Fixed).
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CARD SET 7 MATERIAL CARDS—Three cards for each different material, a total of NMATS\*3 cards.
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1st Card MATERIAL IDENTIFICATION CARD (I5)
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Cols. 1-5 NUMAT Material identification number.
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2nd Card MATERIAL PROPERTIES CARD—(a) (8E10.4)
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Cols. 1-10 PROPS(NUMAT,1) Young's Modulus, $E$ .
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11-20 PROPS(NUMAT,2) Poisson's ratio, $\nu$ .
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21-30 PROPS(NUMAT,3) Thickness for plane stress problem, t.
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31-40 PROPS(NUMAT,4) Mass density per unit volume, $\rho$ .
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41-50 PROPS(NUMAT,5) Temperature coefficient, $\alpha_{t}$ .
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51-60 PROPS(NUMAT,6) Reference yield value $F_{0}$ :
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Von Mises, $F_0 = \sigma Y,$
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Tresca, $F_{0} = \sigma_{Y},$
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Mohr-Coulomb, $F_0 = c\cos \phi$
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Drucker-Prager, $F_{0} = 6c\cos \phi /$
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$(\sqrt{3}(3 - \sin \phi)).$
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61-70 PROPS(NUMAT,7) Hardening parameter, $H'$ :
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$$
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H ^ {\prime} = \frac {E _ {T}}{1 - E _ {T} / E},
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$$
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where $E_{T}$ is the hardening tangent modulus,
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$E$ is the tangent modulus,
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$\sigma_{Y}$ is the yield stress,
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$c$ is the cohesion,
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$\phi$ is the friction angle.
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71-80 PROPS(NUMAT,8) Friction angle ‘ $\phi$ ’.
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<!-- source-page: 534 -->
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3rd Card MATERIAL PROPERTIES CARD—(b) (3E10.4)
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Cols. 1–10 PROPS(NUMAT,9) Fluidity parameter, γ.
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11-20 PROPS(NUMAT,10)Exponent, $\delta$ .
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21-30 PROPS(NUMAT,11)NFLOW code
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(NFLOW = 1—Power law,
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NFLOW ≠ 1—Exponential law).
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CARD SET 8 TIME INTEGRATION CONTROL CARD (1115)—One card.
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Cols. 1–5 NSTEP Total number of time steps.
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6-10 NOUTD Writes displacement and stress history of required points on tapes 10 and 11 respectively at NOUTD timesteps.
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11-15 NOUTP Output for displacements and stresses at every NOUTP step (NOUTP $\leqslant 500$ ).
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16-20 NREQD Number of nodes for selective output of displacements at NOUTD steps.
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21-25 NREQS Number of integration points for selective output of stresses at every NOUTP step.
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26-30 NACCE Number of acceleration ordinates (If IFUNC $\neq 0$ , NACCE is not used, then leave blank).
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31-35 IFUNC Time function code:
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IFUNC = 0 Acceleration time history, IFUNC = 1 Heaviside function, $f(t) = 1.0$ ,
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IFUNC = 2 Harmonic excitation, $f(t)$ $= a_{0} + b_{0} \sin \omega t.$
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36-40 IFIXD Indicator for excitation:
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IFIXD = 0, Horizontal acceleration read from tape 7, Vertical acceleration read from tape 12.
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IFIXD = 1, Vertical acceleration read from tape 12,
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IFIXD = 2, Horizontal acceleration read from tape 7. (If IFUNC ≠ 0 IFIXD is not used, then leave blank.)
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41-45 MITER Maximum number of iterations. This variable is not used in DYNPAK, so leave blank.
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<!-- source-page: 535 -->
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46-50 KSTEP
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Number of steps after which the stiffness matrix is reformed. Not used in DYN-PAK, leave blank.
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51-55 IPRED
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= 1 Standard algorithm,
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= 2 Modified algorithm.
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CARD SET 9 TIME INTEGRATION PARAMETERS CARD (8F10.3)—Two cards.
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1st Card
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Cols. 1-10 DTIME
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11-20 DTEND
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21-30 DTREC
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31-40 AALFA
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41-50 BEETA
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51-60 DELTA
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61-70 GAAMA
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71-80 AZERO
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2nd Card
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1-10 BZERO
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11-20 OMEGA
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21-30 TOLER
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Time step length.
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Time at the end of the excitation force.
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Time step of acceleration records.
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$\alpha = \text{Damping} \quad \text{parameter}, \quad C = \alpha M,$ $\alpha = 2\xi_i\omega_i.$
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$\beta = \text{Damping parameter}, C = \beta K.$ $(\alpha + \beta \omega_{i}^{2} = 2\omega_{i}\xi_{i}, \text{not used in DYNPAK})$
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Newmark's integration parameter $(\delta = 0.25 (\gamma + 0.5)^2$ , not used in DYN-PAK).
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Newmark's integration parameter ( $\gamma \geqslant 0.5$ for stable solution, not used in DYN-PAK).
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Constants for harmonic excitation $f(t) = a_{0} + b_{0} \sin \omega t$ .
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Specified tolerance (Not used in DYN-PAK).
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CARD SET 10 CARD FOR NODAL POINTS FOR WHICH DISPLACEMENT HISTORY IS REQUIRED (16I5)—Total of NREQD nodes.
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Cols. 1-5 NPRQD(1)
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6-10 NPRQD(2)
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First nodal point at which displacement history is required.
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Second nodal point at which displacement history is required.
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11-15 .
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<!-- source-page: 536 -->
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CARD SET 11 CARD FOR INTEGRATION POINTS FOR WHICH STRESS HISTORY IS REQUIRED (16I5)—Total of NREQS integration points.
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Cols. 1-5 NGRQS(1)
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First integration point at which stress history is required.
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6-10 NGRQS(2)
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Second integration point at which stress history is required.
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11-15 .
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. .
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. .
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. .
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. .
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CARD SET 12 IMPLICIT-EXPLICIT ELEMENT INDICATOR CARDS (16I5). Number of cards depends on number of elements. For each 16 elements one card is needed. In DYNPAK, INTGR(IELEM) is 2 for every element.
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INTGR(IELEM) = 1, Implicit element.
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INTGR(IELEM) = 2, Explicit element.
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CARD SET 13 INITIAL DISPLACEMENT CARDS (I5,2F10.5)—One card for each node. If all displacements are zero, read data for last node.
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Cols. 1–5 NGASH
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Nodal point.
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6-15 XGASH
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Initial $x$ -displacement.
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16-25 YGASH
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Initial y-displacement.
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CARD SET 14 INITIAL VELOCITY CARDS (15,2F10.5)—One card for each node. If all velocities are zero, read data for last node.
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Cols. 1–5 NGASH
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Nodal point.
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6-15 XGASH
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Initial $x$ -velocity.
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16-25 YGASH
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Initial y-velocity.
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CARD SET 15 PREVIOUS LOAD STATE CARDS (15,2F10.3)—One card for one node, a total of NNODE cards. Data for the last nodal point should always be read even when it is not loaded. If NPREV = 0 then omit this set of data.
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Cols. 1-5 NGASH
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Nodal point.
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6-15 XGASH
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Equivalent nodal load in $x$ direction.
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16-25 YGASH
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Equivalent nodal load in $y$ direction.
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CARD SET 16 PREVIOUS STRESS STATE CARD (I5,4F10.3)—One card for one integration point. Total of (NELEM\*NGAUS\*NGAUS) cards. If NPREV = 0 omit this set of data.
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<!-- source-page: 537 -->
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<table><tr><td>Cols.</td><td>1-5</td><td>KGAUS</td><td>Integration point.</td></tr><tr><td></td><td>6-15</td><td>STRESS(1)</td><td>Initial stress, $\sigma_x$ or $\sigma_r$ .</td></tr><tr><td></td><td>16-25</td><td>STRESS(2)</td><td>Initial stress, $\sigma_y$ or $\sigma_z$ .</td></tr><tr><td></td><td>26-35</td><td>STRESS(3)</td><td>Initial stress, $\gamma_{xy}$ or $\gamma_{rz}$ .</td></tr><tr><td></td><td>36-45</td><td>STRESS(4)</td><td>Initial stress, $\sigma_z$ or $\sigma_\theta$ .</td></tr></table>
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CARD SET 17 LOAD TITLE CARD (10A4)—One card.
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Cols. 1–40 Title of load applied—limited to 40 alphanumeric characters.
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CARD SET 18 LOAD INDICATOR CARD (415)—One card.
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<table><tr><td>Cols.</td><td>1-5</td><td>IPLOD</td><td>Point load indicator.</td></tr><tr><td></td><td>6-10</td><td>IGRAV</td><td>Gravity load indicator.</td></tr><tr><td></td><td>11-15</td><td>IEDGE</td><td>Edge load indicator.</td></tr><tr><td></td><td>16-20</td><td>ITEMP</td><td>Temperature load indicator.</td></tr></table>
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CARD SET 19 POINT LOAD CARD (I5,2F10.3)—One card for each node. Data for the last node must be specified at the end. If IPLOD = 0 then omit this set of data.
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<table><tr><td>Cols.</td><td>1-5</td><td>LODPT</td><td>Node number.</td></tr><tr><td></td><td>6-15</td><td>POINT(1)</td><td>Load in x-direction.</td></tr><tr><td></td><td>16-25</td><td>POINT(2)</td><td>Load in y-direction.</td></tr></table>
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CARD SET 20 GRAVITY LOAD CARD (2F10.3)—One card only. If IGRAV = 0 then omit this set of data.
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<table><tr><td>Cols. 1-10 THETA</td><td>Angle of gravity axis to the positive y axis.</td></tr><tr><td>11-20 GRAVY</td><td>Gravity constant.</td></tr></table>
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CARD SET 21 NUMBER OF PRESSURE EDGE CARD (I5)—One card. If IEDGE = 0, then omit card sets 21 and 22.
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Cols. 1-5 NEDGE Number of loaded edges.
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CARD SET 22 PRESSURE CARDS—Two cards for each pressure loaded edge.
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1st Card PRESSURE NODES CARD (415)—One card for each edge. Total of NEDGE cards.
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<table><tr><td>Cols. 1-5 NEASS</td><td>Element number with edge load.</td></tr><tr><td>Cols. 6-10 NOPRS(1)</td><td rowspan="3">Edge nodes read in anticlockwise sequence.</td></tr><tr><td>11-15 NOPRS(2)</td></tr><tr><td>16-20 NOPRS(3)</td></tr></table>
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<!-- source-page: 538 -->
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2nd Card PRESSURE CARD (6F10.3)—One card for each edge. Total of NEDGE cards. A pressure normal to a face is assumed to be positive if it acts in a direction into the element. A tangential load is assumed to be positive if it acts in an anticlockwise direction with respect to the loanedWW positive if it acts in an anticlockwise direction with respect to the loaded element.
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Cols. 1-10 PRESS(1,1) } Normal component of edge load for each node.
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11-20 PRESS(2,1)
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21-30 PRESS(3,1)
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31-40 PRESS(1,2)
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41-50 PRESS(2,2)
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51-60 PRESS(3,2) } Tangential component of edge load for each node.
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CARD SET 24 TEMPERATURE CARDS (I5, F10.3)—One card for each node. The last card must be for the highest numbered node. If $\text{ITEMP} = 0$ , omit this set of data.
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Cols. 1–5 NODPT Node number.
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6–15 TEMPE Nodal temperature.
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CARD SET 25 CONCENTRATED MASSES (I5,2F10.3)—One card for each node. Total of NCONM cards. If NCONM = 0, omit this set of data.
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Cols. 1–5 IPOIN Current nodal point with concentrated mass.
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6–15 XCMAS Concentrated mass associated with the x-direction.
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16–25 YCMAS Concentrated mass associated with the y-direction.
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<!-- source-page: 539 -->
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# Appendix IV
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# Sample input data and line printer output for one – and two-dimensional applications
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In this appendix input data and line printer output are provided for a selection of the numerical examples presented in the text. This information will be of assistance to readers who wish to implement the programs contained in the book on their own computer. For economy of space, presentation is limited to one example from each area of application. Also in some cases the line printer output is edited for the same reason.
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# A.4.1 Solution of one-dimensional quasiharmonic problem by direct iteration. Example of Section 3.9.3, Fig. 3.3
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Input data
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<table><tr><td colspan="9">1-D QUASIHARMONIC EXAMPLE, SECTION 3.9.3, FIG. 3.3</td></tr><tr><td>11</td><td>10</td><td>2</td><td>1</td><td>1</td><td>2</td><td>1</td><td>1</td><td>1</td></tr><tr><td></td><td>1</td><td></td><td>10.0</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1</td><td>1</td><td>2</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>2</td><td>2</td><td>3</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>3</td><td>3</td><td>4</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>4</td><td>4</td><td>5</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>5</td><td>5</td><td>6</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>6</td><td>6</td><td>7</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>7</td><td>7</td><td>8</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>8</td><td>8</td><td>9</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>9</td><td>9</td><td>10</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>10</td><td>10</td><td>11</td><td>1</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>1</td><td>0.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>2</td><td>1.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>3</td><td>2.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>4</td><td>3.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>5</td><td>4.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>6</td><td>5.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>7</td><td>6.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>8</td><td>7.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>9</td><td>8.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>10</td><td>9.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>11</td><td>10.0</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>1</td><td>1</td><td>0.0</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>11</td><td>1</td><td>1.0</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>10</td><td></td><td>0.0</td><td></td><td></td><td>0.0</td><td></td><td></td></tr><tr><td>20</td><td>1</td><td></td><td>1.0</td><td></td><td></td><td>0.5</td><td></td><td></td></tr></table>
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<table><tr><td colspan="8">1-D QUASIHARMONIC EXAMPLE, SECTION 3.9.3, FIG. 3.3</td></tr><tr><td colspan="8">NPOIN = 11 NELEM = 10 NBOUN = 2 NMATS = 1</td></tr><tr><td colspan="8">NPROP = 1 NNODE = 2 NINCS = 1 NALGO = 1</td></tr><tr><td colspan="8">NDOFN = 1</td></tr><tr><td colspan="8">MATERIAL PROPERTIES</td></tr><tr><td colspan="8">1 10.00000</td></tr><tr><td colspan="8">EL NODES MAT.</td></tr><tr><td colspan="8">1 1 2 1</td></tr><tr><td colspan="8">2 2 3 1</td></tr><tr><td colspan="8">3 3 4 1</td></tr><tr><td colspan="8">4 4 5 1</td></tr><tr><td colspan="8">5 5 6 1</td></tr><tr><td colspan="8">6 6 7 1</td></tr><tr><td colspan="8">7 7 8 1</td></tr><tr><td colspan="8">8 8 9 1</td></tr><tr><td colspan="8">9 9 10 1</td></tr><tr><td colspan="8">10 10 11 1</td></tr><tr><td colspan="8">NODE COORD.</td></tr><tr><td colspan="8">1 0.00000</td></tr><tr><td colspan="8">2 1.00000</td></tr><tr><td colspan="8">3 2.00000</td></tr><tr><td colspan="8">4 3.00000</td></tr><tr><td colspan="8">5 4.00000</td></tr><tr><td colspan="8">6 5.00000</td></tr><tr><td colspan="8">7 6.00000</td></tr><tr><td colspan="8">8 7.00000</td></tr><tr><td colspan="8">9 8.00000</td></tr><tr><td colspan="8">10 9.00000</td></tr><tr><td colspan="8">11 10.00000</td></tr><tr><td colspan="8">RES. NODE CODE PRES. VALUES</td></tr><tr><td colspan="8">1 1 0.00000</td></tr><tr><td colspan="8">11 1 1.00000</td></tr><tr><td colspan="8">ELEMENT NODAL LOADS</td></tr><tr><td colspan="8">1 0.00000 0.00000</td></tr><tr><td colspan="8">2 0.00000 0.00000</td></tr><tr><td colspan="8">3 0.00000 0.00000</td></tr><tr><td colspan="8">4 0.00000 0.00000</td></tr><tr><td colspan="8">5 0.00000 0.00000</td></tr><tr><td colspan="8">6 0.00000 0.00000</td></tr><tr><td colspan="8">7 0.00000 0.00000</td></tr><tr><td colspan="8">8 0.00000 0.00000</td></tr><tr><td colspan="8">9 0.00000 0.00000</td></tr><tr><td colspan="8">10 0.00000 0.00000</td></tr><tr><td colspan="8">IINCS = 1 NITER = 20 NOUTP = 1 FACTO = 0.100000E 01 TOLER = 0.500000E 00</td></tr><tr><td colspan="8">CONVERGENCE CODE = 1 NORM OF RESIDUAL SUM RATIO = 0.000000E 00</td></tr><tr><td colspan="8">NODE DISPL. REACTIONS</td></tr><tr><td colspan="8">1 0.000000E 00 -0.100000E 01</td></tr><tr><td colspan="8">2 0.100000E 00 0.000000E 00</td></tr><tr><td colspan="8">3 0.200000E 00 0.000000E 00</td></tr><tr><td colspan="8">4 0.300000E 00 0.000000E 00</td></tr><tr><td colspan="8">5 0.400000E 00 0.000000E 00</td></tr><tr><td colspan="8">6 0.500000E 00 0.000000E 00</td></tr><tr><td colspan="8">7 0.600000E 00 0.000000E 00</td></tr><tr><td colspan="8">8 0.700000E 00 0.000000E 00</td></tr><tr><td colspan="8">9 0.800000E 00 0.000000E 00</td></tr><tr><td colspan="8">10 0.900000E 00 0.000000E 00</td></tr><tr><td colspan="8">11 0.100000E 01 0.100000E 01</td></tr><tr><td colspan="8">ELEMENT STRESSES PL.STRAIN</td></tr><tr><td colspan="8">1 0.000000E 00 0.000000E 00</td></tr><tr><td colspan="8">2 0.000000E 00 0.000000E 00</td></tr><tr><td colspan="8">3 0.000000E 00 0.000000E 00</td></tr><tr><td colspan="8">4 0.000000E 00 0.000000E 00</td></tr><tr><td colspan="8">5 0.000000E 00 0.000000E 00</td></tr></table>
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