CALCS | BAS012 MATRIX STIFFNESS ANALYSIS |

## APPLICATIONThe program obtains solutions to structural analysis tasks within the following boundaries:For problems ouside of these boundaries recourse to full Finite Element Analysis is suggested. ## OUTPUTNodal Displacements, Reactions and Element Internal loadsProblem definition plot showing nodes & elements ## SEE ALSOBAS020## THEORYFinite Element Method | |

## KEYWORDS | |

JTITLE | job title |

CCOMB | case, combination |

CDISP | case, displacement set |

CLOAD | case, load set |

CTITLE | case, title |

CUNIT | case, unit |

DMPC | displacement, multi-point constraint |

DSPC | displacement, single point constraint |

EBAR | element, bar |

EELR | element, elastic load reaction |

ENDDAT | input file terminator marker |

EPB | element, shear & biaxial stress panel |

EPS | element, shear panel |

EROD | element, rod |

EROPE | element, rope |

LACCEL | acceleration |

LBAR | load, bar |

LNODE | load, nodal |

NO | node, orientation |

NS | node, structural |

PBAR | property, bar |

PMAT | property, isotropic material |

PPANEL | property, shear panel & shear&biaxialstress panel |

PROD | property, rod |

PROPE | property, rope |

REM | remarks at any points in the input file |

SOL | solution control |

## DATA ELEMENTS | |

A | area, cross section |

CAS | case, comb or unit |

CSET | case set |

DSET | displacement, prescribed set |

E | young's modulus |

En | entity id number |

FD | freedom, dependent |

FI | freedom, independent |

G | shear modulus |

Iy Iz | 2nd MoA about y & z local axes |

J | shear constant, of cross section |

K | factor |

Kt Kr | stiffness- translation or rotation |

L1 to L6 | loads, corresponding to freedoms 1 to 6 |

LSET | load set |

M | moment |

MN | mass, nodal |

ND | node, dependent |

NI | node, independent id |

NPARTS | number of rope parts connecting two nodes |

NSET | node set |

OD | displacement output, 0 or 1 |

OE | element output, 0 or 1 |

P | force |

ROPE | identity, rope |

T | thickness , area |

UDLx y | udl's applied to bar local xy & xz planes |

UTM | upper triangular matrix |

v | poisson's ratio |

X Y Z | global coordinates |

x y z | local coordinates |

## GUIDANCE | |||||||||

## REM | text | ||||||||

Remark cards may be placed anywhere in the input file and form no part of the analysis data | |||||||||

## JTITLE | job title | ||||||||

The job title appears in the headers of the output file | |||||||||

## CDISP | CSET | DSET | |||||||

CSET must be a CUNIT type case More than one displacement set DSET may be referenced | |||||||||

## CLOAD | CSET | LSET | |||||||

CSET must be a CUNIT type case. More than one load set LSET may be referenced. | |||||||||

## CTITLE | CSET | case title | |||||||

CSET may be CUNIT or CCOMB type cases | |||||||||

## CUNIT | CSET | UTM | |||||||

The stiffness matrix is modified by a prescribed displacement set having the corresponding case number and the resulting decomposed matrix remains resident for writing the solution displacement vector file providing the upper triangular matrix ID is unchanged from that immediately preceding it (no DSET change). Thereby, when solving for unit cases the stiffness matrix is not repeatedly decomposed unnecessarily but the solution displacement vector is calculated from scratch. | |||||||||

## CCOMB | CSET | CASE | K | ||||||

No stiffness matrix decomposition is invoked. Cards having the same CSET may be used in a single block enabling superposition of any number of factored cases. CASE may be any preceding CUNIT or CCOMB cards. The solution displacement vector is calculated as the sum of factored preceding cases, CASE may be either CUNIT or CCOMB types. | |||||||||

## NO | NSET | En | X | Y | Z | ||||

Node IDs may be in the range 1 to 50. Orientation nodes do not form part of the problem. IDs must not duplicate NS IDs. They are typically used to orientate elastic reaction axes and bar element planes. | |||||||||

## NS | NSET | En | X | Y | Z | MN | |||

Node IDs may be in the range 1 to 400. Structural nodes provide the freedoms on which any solution is based. Major axis freedoms are: 1-3 translations parallel to X Y & Z axes 4-6 rotations about axes parallel to X Y & Z axes. The present formulation provides for IDs in the range 1 to 400. Nodal Coordinates- Mutually perpendicular position coordinate vectors of the node relative to a datum point parallel to the major axes and in the order X Y & Z form a right handed set. If bars form part of the structure the number of freedoms per node is six, otherwise three. The object of this adjustment is to minimise the number of freedoms, solution time and data storage requirements. Stiffness matrix bandwidth is a function of element connectivity and the order in which the nodes are listed in the input data file. This order may therefore be manipulated to minimise bandwidth. | |||||||||

## PMAT | En | E | G | v | |||||

Material IDs may be in the range 1 to 50. Materials are intended to be isotropic and homogenous through elements. The present formulation does not use the relationship G=E/(2*(1+v)) This may be useful where panel stiffnesses must reflect the effect of modifying influences such as stiffeners, lightening or access holes. | |||||||||

## PROD | En | A | |||||||

Rod property data. Property IDs may be in the range 1 to 50. | |||||||||

## PBAR | En | A | I1 | I2 | J | ||||

Bar property data Property IDs may be in the range 1 to 50. Properties may be zero. | |||||||||

## PPANEL | En | T | |||||||

Panel property data, use for EPS and EPB Property IDs may be in the range 1 to 50. | |||||||||

## PROPE | ROPE | K | A | E | |||||

Property card associated with EROPE element. K.A.E is the rope stiffness per unit length and is the product of an effectivity factor, which accounts for rope fibre cross section fill density and rope twist flexibility, the nominal cross section and Young's Modulus. K is typically taken to be 0.3 A maximum of 10 cards may be used. | |||||||||

## EELR | En | N1 | N2 | Kt | Kr | ||||

Constraint of a structure at a node- force or torque. N1 must be a structural node. N2 may be a structural or orientation node. Contribution to the stiffness matrix is made only at N1. Kt or Kr may be zero. | |||||||||

## EROD | En | N1 | N2 | PMAT | PROD | ||||

Structural element capable of transmitting axial force. N1 and N2 must be structural nodes. PMAT referred to must have a non-zero value for Young's Modulus. | |||||||||

## EBAR | En | N1 | N2 | N3 | PMAT | PBAR | |||

Structural element capable of transmitting moment and shear in two mutually perpendicular planes, axial force and torque. N1 and N2 must be structural nodes. N3 may be a structural or orientation node. Contribution to the stiffness matrix is made at N1 and N2. PMAT referred to must have a non-zero value for Young's Modulus. | |||||||||

## EPS | En | N1 | N2 | N3 | N4 | PMAT | PPANEL | ||

Structural element of quadrilateral form capable of transmitting in-plane membrane shear force. N1 to N4 must be structural nodes. PMAT referred to must have a non-zero value for the shear modulus. N1 to N4 must lie in a flat plane as this is assumed in the formulation. | |||||||||

## EPB | En | N1 | N2 | N3 | N4 | PMAT | PPANEL | ||

Structural element of quadrilateral form capable of transmitting in-plane membrane shear and biaxial loads. N1 to N4 must be structural nodes. PMAT referred to must have a non-zero value for Young's Modulus, the shear modulus and Poisson's ratio. N1 to N4 must lie in a flat plane as this is assumed in the formulation. | |||||||||

## EROPE | ROPE | N1 | N2 | NPARTS | |||||

Structural element in which the the axial force acting in all rope parts (connecting two nodes) is equal. This is an idealisation of a multiple part rope/sheaves combination. Multiple EROPE cards may be used to define the parts composing any single rope and up to ten ropes may be used, with ROPE ids in the range 1 to 10. ROPE ids must correspond with those used on PROPE cards. This element will often prove to oppose formulating compact banded solutions as a rope may cover large areas of structure modelled with elements more 'bandwidth' friendly. The memory usage associated with the use of this element must be accounted for when building a model. In the present formulation sheave radii are not used because of difficulty in determining the points of impingement of rope parts on sheaves. Is is considered that this limitation will only infrequently be significant, when a rope part connects two closely spaced large diameter sheaves. Sheave 'friction', typically taken to be in the range 2 to 4% is not implimented but this will typically not be significant. The NPARTS term allows multiple parts connecting the same two nodes to be defined without using more than one card. When this factor is greater than unity it increases rope length and hence flexibility & the force acting between two nodes but does not increase rope stiffness. | |||||||||

## DMPC | DSET | ND | FD | NI | FI | K | |||

In which the freedoms of a node are constrained by a relationship of the form: Aii = Ci.Ai1 ... + Cij.Aij ... + Ci To effect a multi-point constraint use one card for each independent freedom of the equation. Use with CUNIT type cases only. CUNITs may reference more than one DSET. | |||||||||

## DSPC | DSET | NS | F1 | F2 | F3 | F4 | F5 | F6 | |

Prescribed displacements are labled 'F' or 0 or non-zero. Use with CUNIT type cases only. CUNITs may reference more than one DSET. | |||||||||

## LACCEL | LSET | NSET | Kx | Ky | Kz | ||||

Acceleration factors are applied to members of NSET only. It is envisaged that this facility will be most useful when rotational accelerations are incorporated. | |||||||||

## LNODE | LSET | NS | L1 | L2 | L3 | L4 | L5 | L6 | |

Forces and moments parallel to global axes freedoms 1 to 6 applied at a structural node. CUNIT type cases may reference multiple LSETs. Loads 1 to 6 may be zero. | |||||||||

## LBAR | LSET | EBAR | UDLy | UDLz | |||||

Line loads w applied to EBAR parallel to the local y and z axes respectively. CUNIT type cases may reference multiple LSETs. Bars EBAR must be in the same order as EBAR data cards. UDLs y or z may be zero. The formulation assumes that bars referenced contribute to the stiffness matrix. | |||||||||

## SOL | 0 | OD | OE | ||||||

Solution control flags, 0 output off, 1 output on. | |||||||||

## ENDDAT | |||||||||

End of input file marker. | |||||||||

## INPUT FORMAT | |||||||||

Data entries start with a keyword Data components are seperated by TAB characters The required form, content and order of the file is as follows: | |||||||||

DAT012 | |||||||||

SOL | 0 | OD | OE | ||||||

REM | text | ||||||||

JTITLE | job title | ||||||||

CCOMB | CSET | CASE | K | ||||||

CDISP | CSET | DSET | |||||||

CLOAD | CSET | LSET | |||||||

CTITLE | CSET | casetitle | |||||||

CUNIT | CSET | UTM | |||||||

DMPC | DSET | ND | FD | NI | FI | K | |||

DSPC | DSET | NS | F1 | F2 | F3 | F4 | F5 | F6 | |

EBAR | En | N1 | N2 | N3 | MAT | PBAR | |||

EELR | En | N1 | N2 | Kt | Kr | ||||

EPB | En | N1 | N2 | N3 | N4 | MAT | PPANEL | ||

EPS | En | N1 | N2 | N3 | N4 | MAT | PPANEL | ||

EROD | En | N1 | N2 | MAT | PROD | ||||

EROPE | ROPE | N1 | N2 | NPARTS | |||||

LACCEL | LSET | NSET | Kx | Ky | Kz | ||||

LBAR | LSET | EBAR | UDLy | UDLz | |||||

LNODE | LSET | NS | L1 | L2 | L3 | L4 | L5 | L6 | |

NO | NSET | En | X | Y | Z | ||||

NS | NSET | En | X | Y | Z | MN | |||

PBAR | En | A | Iy | Iz | J | ||||

PMAT | En | E | G | v | |||||

PPANEL | En | T | |||||||

PROD | En | A | |||||||

PROPE | ROPE | K | A | E | |||||

ENDDAT | |||||||||

## EXAMPLE | |||||||||

## Input | |||||||||

DAT012 | |||||||||

SOL | 0 | 1 | 1 | ||||||

JTITLE | test case | ||||||||

CDISP | 1 | 1 | |||||||

CLOAD | 1 | 1 | |||||||

CTITLE | 1 | unit load | |||||||

CUNIT | 1 | 1 | |||||||

DSPC | 1 | 1 | 0 | 0 | 0 | F | F | F | |

DSPC | 1 | 4 | 0 | 0 | 0 | F | F | F | |

EROD | 1 | 1 | 2 | 1 | 1 | ||||

EROD | 2 | 2 | 3 | 1 | 1 | ||||

EROD | 3 | 3 | 4 | 1 | 1 | ||||

EROD | 4 | 1 | 3 | 1 | 1 | ||||

EROD | 5 | 2 | 4 | 1 | 1 | ||||

LNODE | 1 | 2 | 0 | -1 | 0 | 0 | 0 | 0 | |

NS | 1 | 1 | 0 | 0 | 0 | 0 | |||

NS | 1 | 2 | 4 | 0 | 0 | 0 | |||

NS | 1 | 3 | 4 | 3 | 0 | 0 | |||

NS | 1 | 4 | 0 | 3 | 0 | 0 | |||

PMAT | 1 | 1 | 1 | 1 | |||||

PROD | 1 | 1 | |||||||

ENDDAT | |||||||||

## Output | |||||||||

BAS012 OUTPUT | |||||||||

BAS012 | RUNTIME Mon,13 Jan 2003.21:37:22 | ||||||||

CTITLE | 1 | unit load | |||||||

NODAL DISPLACEMENTS | |||||||||

CASE | NODE | TX | TY | TZ | RX | RY | RZ | ||

1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ||

1 | 2 | -2.84 | -11.2 | 0 | 0 | 0 | 0 | ||

1 | 3 | 2.49 | -9.8 | 0 | 0 | 0 | 0 | ||

1 | 4 | 0 | 0 | 0 | 0 | 0 | 0 | ||

BAS012 | RUNTIME Mon,13 Jan 2003.21:37:22 | ||||||||

CTITLE | 1 | unit load | |||||||

CASE | EROD | N1 | N2 | P | |||||

1 | 1 | 1 | 2 | -0.711 | |||||

1 | 2 | 2 | 3 | 0.467 | |||||

1 | 3 | 3 | 4 | 0.622 | |||||

1 | 4 | 1 | 3 | -0.778 | |||||

1 | 5 | 2 | 4 | 0.889 | |||||

END012 |