Z88 (z88i1.txt, results z88o2.txt / z88o3.txt / z88o4.txt)

Z88 is an open-source finite element program for teaching and small companies (Z88OS, and the freeware Z88Aurora). Its files have fixed names: the structure file z88i1.txt, then boundary conditions (z88i2.txt), surface loads (z88i5.txt), materials (z88mat.txt and the files it names), element parameters (z88elp.txt), integration orders (z88int.txt) and, after a run, displacements (z88o2.txt), stresses (z88o3.txt) and nodal forces (z88o4.txt).

Format name	z88
File names	z88i1.txt, z88structure.txt (Aurora), and z88o2.txt/z88o3.txt (which read the structure file next to them); any case
Read / Write	✓ / ✓ (structure file and the input files above, except surface loads)
Extra dependencies	—

Reading & writing

import meshioplusplus

mesh = meshioplusplus.read("run/z88i1.txt")          # mesh + results next to it
mesh = meshioplusplus.z88.read("run/z88i1.txt", results=False)
meshioplusplus.write("out/z88i1.txt", mesh)          # or z88.write(..., stubs=True)

The file name decides the format: z88i1.txt is Z88's, although .txt otherwise belongs to xyz. The native resolver and the Python dispatch both check the name first. A structure file under any other name needs file_format="z88".

The structure file

• The header's first three integers are the dimension, the node count and the element count. Z88OS v15 writes ndim nnodes nelem ndof kflag; Z88 up to V13 and Z88Aurora V1 add the material count and more flags, and put one material line per range after the elements, which the reader skips.
• One line per node, id ndof x y [z], and two per element: id type, then its nodes (their count is fixed by the type). Text after the numbers on a line is ignored.
• KFLAG = 1 means cylindrical input (r, φ in degrees, z), converted to Cartesian with a warning.

Z88 type	Element	meshio++ type
1	8-node hexahedron	hexahedron
10	20-node hexahedron	hexahedron20
16 / 17	10- / 4-node tetrahedron	tetra10 / tetra
7, 8, 20, 23	8-node plane, torus, plate, shell	quad8
3, 14, 15, 18, 24	6-node plane, torus, plate, shell	triangle6
6	3-node torus	triangle
2, 4, 5, 9, 13, 25	beams, trusses, shaft	line
11, 12 / 19 / 21 / 22	12-node plane and torus / 16-node plate / 16- and 12-node volume shells	corners only: quad / quad / hexahedron / wedge, with a warning and a provenance note

The Z88 type is kept as the z88:type cell data, so a round trip keeps it.

Node order

• Hexahedra (types 1 and 10) list the face the Z88 manual draws on top first, so read as-is their volume is negative: every hexahedron of the Z88OS examples is. They use the "z88" tables of the node-ordering registry. Z88R ran the hex20 fixture deck and the deck meshio++ writes back from it, and gave identical displacements.
• tet10 lists its last three mid-edge nodes on edges 2-4, 3-4, 1-4 (checked on the mid-edge positions of the Z88OS example b11).
• Everything else is in meshio++'s order (checked on the Z88OS plane, torus and plate examples). The corner choice of the layered shells 21 and 22 follows their shape functions and has not been run through Z88.

The rest of the deck

When the directory holds them, the reader attaches the input files as data (whatever results says), and the writer writes them back from that data:

File	Read as
z88i2.txt	point_data["z88:bc:u"] (prescribed displacements, flag 2) and ["z88:bc:f"] (nodal forces, flag 1, summed when a degree of freedom has several), one column per degree of freedom (2, 3 or 6, the widest node's), NaN where there is no entry. An empty file adds nothing
z88mat.txt and its material files	cell_data["z88:material"] (the file's number, 51 for 51.txt, else its row), ["z88:E"] and ["z88:nu"] (the first line of the material file)
z88elp.txt	cell_data["z88:elp"], 12 columns: QPARA, RIYY, EYY, RIZZ, EZZ, RIT, WT, IFBETI, XCP, YCP, ZCP, RKAP. Fields a row leaves out are NaN (Z88R leaves them untouched, which is not the same as 0)
z88int.txt	cell_data["z88:int"]: INTORD, INTOS; −1 for elements no row names
z88sets.txt (Z88Aurora)	element sets as cell regions and node sets as point regions, named as in Aurora (tag = set id). Surface sets name Aurora's own surface mesh, not the structure file's elements, and are skipped with a warning

Element ranges refer to element ids, node entries to node ids; elements no row names get NaN (or 0, −1). Surface and pressure loads (z88i5.txt) are not read.

Results

With results (the default), the reader also attaches:

• z88o2.txt: point_data["U"] with 2, 3 or 6 columns (the widest node's degrees of freedom; NaN where a node has fewer). The language-dependent header is skipped: data rows are recognised by their shape.
• z88o4.txt: the nodal sums (the last table) as point_data["F"], with the same columns as the constraints.
• z88o3.txt: each element's block has a line of column labels, then one row per corner or Gauss point; each label is averaged over the rows. Solid (1, 10, 16, 17) and plane-stress (3, 7, 11, 14) elements give the stress tensor cell_data["SIG"] (XX YY ZZ XY YZ ZX in 3-D, XX YY XY in 2-D). Every other label becomes a scalar cell array of its name, NaN on elements that do not print it: SIGXX TAUXX SIGYY1 SIGZZ1 SIGYY2 SIGZZ2 for 3-D beams (2, 25), SIGXX SIGZZ1 SIGZZ2 for beams in the plane (13), SIGXX TAUXX SIGXY1 SIGXZ1 SIGXY2 SIGXZ2 for the shaft (5), the axial SIGXX of trusses (4, 9), MXX MYY MXY QYZ QZX SIGXX SIGYY TAUXY TAUXZ TAUYZ for plates (18–20), SIGXX SIGYY TAUXY for shells (23, 24), SIGRR SIGZZ TAURZ SIGTE for tori (6, 8, 12, 15), and SIGRR SIGTT TAURT when plane elements are computed in polar coordinates. The equivalent stress is cell_data["SIGV"] for every family. Coordinate columns (XX, YY, ZZ, RR, PHI) are not kept.

Z88 is linear static, so there are no steps.

Writing

• The Z88OS v15 layout: the five-integer header (the provenance tag follows it on the same line, where Z88 writes its own comment), nodes with their degrees of freedom (the most any of their elements needs), then the elements.
• The element type comes from z88:type when it matches the cell, else from the cell type: hexahedron 1, hexahedron20 10, tetra 17, tetra10 16, triangle6 14 (24 in 3-D), quad8 7 (23 in 3-D), line 9 (4 in 3-D). A 2-D file is written when every z is 0 and no cell is 3-D.
• A 3-D file is also written when a kept z88:type exists only in 3-D files (solids, 3-D beams, trusses and the shaft, shells), so flat frames and shells stay 3-D.
• The z88: arrays above are written back next to the structure file: z88i2.txt, z88mat.txt with one <n>.txt per distinct E and ν (numbered by z88:material when that is free, else 1, 2, …), z88elp.txt (the leading fields up to the first NaN) and z88int.txt, each grouping consecutive elements with equal values into one range.
• stubs=True also writes an empty z88i5.txt, and an empty z88i2.txt when the mesh has no constraints, so the deck is complete.
• Dropped, with a warning and a provenance note: cells with no Z88 type (hexahedron27, pyramids, polygons…), regions (Z88OS has no groups; Aurora's sets file is not written) and other data arrays, results included. A mesh with nothing to write is a WriteError.

Validation

The decks under tests/python/meshes/z88/ are written by tools/gen_z88_fixtures.py; their z88o2.txt/z88o3.txt/z88o4.txt are Z88OS V15's own output (a hex20 cantilever, a frame of 3-D beams and a truss, a plate, flat tri6 shells and an axisymmetric torus). The cantilever's tip deflection, 1.849 mm, is within 3 % of the Euler-Bernoulli value for this coarse mesh; on free degrees of freedom the nodal forces equal the applied loads.

Outside the repository (v16.11.0) Z88R solved the 14 example decks of Z88OS, covering trusses, shafts, beams in the plane, tori, plane stress, plates and shells as well as solids. Both engines read the same arrays from every deck and write the same bytes, and Z88R run on each deck meshio++ writes back gave exactly the same displacements and stresses (the 16-node plate deck, whose elements are read as corner quads, is not writable, and two tetrahedral decks exceed the prebuilt Z88R's memory). A flat deck of 8-node shells (type 23) built for the fixtures failed Z88R's own Jacobian check whatever its orientation, so the shell fixture uses type 24. A public Z88Aurora V2 project (structure file, sets and Z88R V15.0B displacements; not redistributable) was read with its element and node sets.