김경종
18 KiB
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Appendix I
Instructions for preparing input data for one-dimensional problems
In Part I of this text computer codes have been presented for the nonlinear analysis of several classes of one-dimensional problems. In Chapter 3 the data structure for the following applications was discussed:
- Direct iteration solution of nonlinear quasiharmonic problems.
- Use of the Newton–Raphson process for the solution of nonlinear quasiharmonic problems.
● Nonlinear elastic applications. - Elasto-plastic material behaviour.
In Chapter 4 the time transient phenomenon of one-dimensional visco-plasticity was discussed. In Chapter 5 solution techniques were presented for elasto-plastic beam bending problems. In this appendix user instructions for preparing input data for each of these applications are provided.
A.1.1 Program QUITER for the solution of nonlinear one-dimensional quasiharmonic problems by direct iteration
CARD SET 1 TITLE CARD (12A6)—One card
Cols. 1-72 Title of the problem—limited to 72 alphanumeric characters.
CARD SET 2 CONTROL CARD (915)—One card
Cols. 1-5 NPOIN
6-10 NELEM
11-15 NBOUN
Total number of nodal points.
Total number of elements.
Total number of restrained boundary points—nodes at which the value of the unknown (e.g. temperature) is prescribed.
Total number of different materials.
16-20 NMATS
21-25 NPROP
Number of independent properties per material (= 1).
26-30 NNODE
Number of nodes per element (= 2).
31-35 NINCS
Number of increments in which the total 'loading' is to be applied.
36-40 NALGO Nonlinear solution process indicator (= 1, for solution by direct iteration).
41-45 NDOFN Number of degrees of freedom per node (= 1) .
CARD SET 3 MATERIAL CARDS (I5, F15.5)—One card for each different material. Total of NMATS cards (See Card Set 2).
Cols. 1–5 JMATS Material identification number.
6–20 PROPS(JMATS,1) The material coefficient, K_{0} in (2.27).
CARD SET 4 ELEMENT CARDS (4I5)—One card for each element. Total of NELEM cards (See Card Set 2).
Cols. 1–5 JELEM Element number. 6–10 LNODS(JELEM,1) 1st nodal connection number. 11–15 LNODS(JELEM,2) 2nd nodal connection number. 16–20 MATNO(JELEM) Material property number.
NOTE: The two nodal connection numbers for an element can be taken in any order.
CARD SET 5 NODAL COORDINATE CARDS (I10,F15.5)—One card for each node. Total of NPOIN cards (See Card Set 2).
Cols. 1–10 JPOIN Node number. 11–25 COORD(JPOIN) The x coordinate of the node.
Note: The origin of the coordinate system may be arbitrarily located.
CARD SET 6 RESTRAINED NODE CARDS (I10,I5,F10.5)—One card for each restrained node. Total of NBOUN cards (See Card Set 2).
Cols. 1-10 NODFX Restrained node number.
11-15 ICODE(1) Condition of restraint(=1).
16-25 PRESC(1) The prescribed value of the nodal variable.
CARD SET 7 APPLIED 'LOAD' CARDS (I10,2F15.5)—One card for each loaded element.
Cols. 1–10 IELEM The element-number. 11–25 RLOAD(IELEM,1) The applied load at the 1st node of the element. 26–40 RLOAD(IELEM,2) The applied load at the 2nd node of the element.
Notes: 1) The 1st and 2nd nodes must be taken in the order listed in Card Set 4. 2) This card set must terminate with data for the highest numbered element whether it is loaded or not.
CARD SET 8 LOAD INCREMENT CONTROL CARDS (2I5,2F15.5)—One card for each load increment. Total of NINCS cards (See Card Set 2).
| Cols. 1-5 NITER | Maximum number of iterations allowed for the ‘load’ increment. |
| 6-10 NOUTP | Output control parameter:1—Results output only after the first iteration and after convergence,2—Results output after each iteration. |
| 11-25 FACTO | Applied ‘load’ factor for the increment—specified as a factor of the loading input in Card Set 7. |
| 26-40 TOLER | Convergence tolerance factor.—The term TOLER in (3.21). |
Note: The applied loading factors are accumulative. If FACTO is specified as 0.6, 0.3, 0.3 for the first three 'load' increments, then the total loading acting during the third increment is 1.2 times that specified in Card Set 7.
If the form of the material nonlinearity is to be changed, then FUNCTION VARIA must be modified in accordance with the process described in Section 3.9.1.
A.1.2 Program QUNEWT for the solution of nonlinear one-dimensional quasiharmonic problems by the Newton–Raphson process
Data input for this application is identical to that described in Section A.1.1 above with the following exceptions:
CARD SET 2 CONTROL CARD
| Cols. 21–25 NPROP | Number of independent properties per material (= 2). |
| 36–40 NALGO | Nonlinear solution process parameter (= 2, for Newton–Raphson solution technique). |
CARD SET 3 MATERIAL CARDS (I5,2F15.5)—One card for each different material.
| Cols. | 1-5 | JMATS | Material identification number. |
| 6-20 | PROPS(JMATS,1) | The material coefficient $K_0$ in (2.27). | |
| 21-35 | PROPS(JMATS,2) | The term $b$ in (2.27). |
A.1.3 Program NONLAS for the solution of one-dimensional nonlinear elastic problems
The input data for this application is again identical to that described in Section A.1.1 with the following exceptions. The basic nodal variable is now the axial displacement.
CARD SET 2 CONTROL CARD
| Cols. 21–25 NPROP | Number of independent properties per material(= 2). |
| 36–40 NALGO | Nonlinear solution process indicator:1 or 2 Tangential stiffness algorithm. The element stiffnesses are recalculated for each iteration of the solution process.3 Initial stiffness method. The stiffnesses are calculated at the beginning of the solution process and maintained constant thereafter.4 Combined algorithm (Version I). The element stiffnesses are recomputed for the first iteration of each load increment.5 Combined algorithm (Version II). The element stiffnesses are recomputed for the second iteration of each load increment. |
CARD SET 3 MATERIAL CARDS (I5,2F15,5)—One card for each different material.
| Cols. | 1-10 | JMATS | Material identification number. |
| 6-20 | PROPS(JMATS,1) | Elastic modulus, $E$ . | |
| 21-35 | PROPS(JMATS,2) | Cross-sectional area, $A$ . |
A.1.4 Program ELPLAS for the solution of one-dimensional elastoplastic problems
The input data for this application is again identical to that described in Section A.1.1 with the following exceptions. The basic nodal variable is the axial displacement.
CARD SET 2 CONTROL CARD (9I5)
| Cols. 21-25 NPROP | Number of independent properties per material (= 4). |
| 36-40 NALGO | Nonlinear solution process indicator: 1 or 2 Tangential stiffness algorithm. |
3 Initial stiffness method.
4 Combined algorithm with stiffnesses recomputed for the 1st iteration.
5 Combined algorithm with stiffnesses recomputed for the 2nd iteration.
CARD SET 3 MATERIAL CARDS (15,4F15.5)—One card for each different material.
| Cols. | 1-5 | JMATS | Material identification number. |
| 6-20 | PROPS(JMATS,1) | Elastic modulus, $E$ . | |
| 21-35 | PROPS(JMATS,2) | Cross-sectional area, $A$ . | |
| 36-50 | PROPS(JMATS,3) | Uniaxial yield stress, $\sigma_{Y}$ . | |
| 51-65 | PROPS(JMATS,4) | Linear strain-hardening parameter, $H'$ . |
A.1.5 Program UNVIS for the solution of one-dimensional elastoviscoplastic problems
The input data for this application is once again identical to that described in Section A.1.1 with the following exceptions. The basic nodal variable is the axial displacement.
CARD SET 2 CONTROL CARD
| Cols. 21-25 NPROP | Number of independent properties per material (= 5). |
| 36-40 NALGO | Nonlinear solution process indicator (= 1, for Euler time stepping scheme). |
CARD SET 3 MATERIAL CARDS (I5,5F15.5)—One card for each different material.
| Cols. | 1-5 | JMATS | Material identification number. |
| 6-20 | PROPS(JMATS,1) | Elastic modulus, $E$ . | |
| 21-35 | PROPS(JMATS,2) | Cross-sectional area, $A$ . | |
| 36-50 | PROPS(JMATS,3) | Uniaxial yield stress, $\sigma_{Y}$ . | |
| 51-65 | PROPS(JMATS,4) | Linear strain-hardening parameter, $H'$ . | |
| 66-80 | PROPS(JMATS,5) | Fluidity parameter, $\gamma$ . |
CARD SET 8 TIMESTEPPING PARAMETER CARD (3F15.5)—One card.
| Cols. 1–15 TAUFT | The factor $\tau$ employed to limit the time-step length according to (4.38). |
| 16–30 DTINT | The initial time step length (required to initiate the time stepping process. |
| 31–45 FTIME | The factor $k$ in (4.39). |
CARD SET 9 LOAD INCREMENT CONTROL CARDS
This card set is identical to Card Set 8, Section A.1.1 where the term 'iteration' is now replaced by 'timestep'.
A.1.6 Program TIMOSH for the nonlayered elasto-plastic analysis of Timoshenko beams
The input data for this application is identical to that described in Section A.1.1 with the following exceptions.
CARD SET 2 CONTROL CARD (9I5)
| Cols. | 21-25 | NPROP | Number of independent properties per material (=4) |
| 36-40 | NALGO | Nonlinear solution process indicator:1 or 2 Tangential stiffness algorithm.3 Initial stiffness method.4 Combined algorithm with stiffnesses recomputed for the 1st iteration.5 Combined algorithm with stiffnesses recomputed for the 2nd iteration. | |
| 41-45 | NDOFN | Number of degrees of freedom per node (=2). |
CARD SET 3 MATERIAL CARDS (I5, 4F15.5)—One card for each different material.
Cols. 6–20 PROPS(JMATS, 1) Flexural rigidity, EI.
21-35 PROPS(JMATS,2) Shear constant, GA/1.5.
36-50 PROPS(JMATS, 3) Yield moment, M_0 .
51-65 PROPS(JMATS, 4) Strain hardening parameter, H' .
CARD SET 6 RESTRAINED NODE CARDS (I10, 2(I5, F10.5))—One card for each restrained node. Total of NBOUN cards.
| Cols. 11-15 | ICODE(1) | Condition of restraint on nodal displacement, w. |
| 0-No displacement restraint. | ||
| 1-Nodal displacement restrained. | ||
| 16-25 | VALUE(1) | The prescribed value of nodal displacement, w. |
| 26-30 | ICODE(2) | Condition of restraint on nodal rotation, θ. |
| 0-No rotation restraint. | ||
| 1-Nodal rotation restrained. | ||
| 31-40 | VALUE(2) | The prescribed value of nodal rotation, θ. |
CARD SET 7 APPLIED LOAD CARDS (I10, 4FI5.5)—One card for each loaded element.
Cols. 1-10 JELEM Element number.
11-25 RLOAD(JELEM,1) Transverse load applied at the first node.
26-40 RLOAD(JELEM,2) Couple applied at the first node.
41-55 RLOAD(JELEM,3) Transverse load applied at the second node.
56-70 RLOAD(JELEM,4) Couple applied at the second node.
Note: The last card should be that for the highest numbered element whether it is loaded or not.
A.1.7 Program TIMLAY for the layered elasto-plastic analysis of Timoshenko beams
The input data for this application is identical to that described in Section A.1.6 with the following exceptions.
CARD SET 2 CONTROL CARD (10I5)
Cols. 21–25 NPROP
Number of independent properties per material ( =4+2\times Total number of layers).
46-50 NLAYR
Total number of layers.
CARD SET 3 MATERIAL CARDS
1st Card (I5, 4F15.5)
Cols. 1–5 NUMAT Material identification number.
6-20 PROPS(NUMAT,1) Young's modulus, E .
21-35 PROPS(NUMAT,2)Modified shear modulus, G / 1.5 .
36-50 PROPS(NUMAT,3) Yield stress, \sigma_{Y} .
51-65 PROPS(NUMAT,4)Strain hardening parameter, H' .
2nd and subsequent cards (4F15.5)
Cols. 1–15 BRDTH(1) Breadth of the 1st layer.
16-30 THICK(1) Thickness of the 1st layer.
31-45 BRDTH(2) Breadth of the 2nd layer.
• • • • • •
BRDTH(NLAYR) Breadth of the last layer.
• THICK(NLAYR) Thickness of the last layer.