Computational Structural Analysis

A Fortran 90 finite element analysis package for 2D frame structures and isoparametric quadrilateral (ISOP4) continuum elements, with MATLAB-based visualization.

Sample Results

Frame Analysis — Bridge Deformed Shape

Multi-span bridge structure with roller supports showing the deformed shape (cyan) against the undeformed geometry (white dashed). Max vertical displacement: 9.98 mm.

ISOP4 Element Analysis — Mesh Deformation

1600-element quadrilateral mesh (1681 nodes) showing deformed shape (red) overlaid on the original geometry (cyan) under applied loading.

ISOP4 Element Analysis — Stress Contour (SIGx)

Normal stress distribution (SIGx) across the plate, with color-mapped contours ranging from +55 to -275 kN/m². Stress concentration visible at the bottom support region.

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Modules

Frame Analysis (CSA_2021_FRAME/)

Solves 2D beam/frame problems using Timoshenko beam theory (includes shear deformation). Each node carries 3 degrees of freedom: horizontal displacement, vertical displacement, and rotation.

Capabilities:

• Distributed loads (constant and linearly varying)
• Thermal effects (uniform temperature change and gradient)
• Prestressing forces with eccentric cable profiles
• Elastic supports and inter-node links
• Internal hinges and roller releases
• Imposed displacements (absolute and relative)
• Self-weight

ISOP4 Element Analysis (CSA_2021_ISOP4/)

Solves 2D continuum problems using 4-node isoparametric quadrilateral elements with 2 DOF per node. Supports both plane stress and plane strain formulations.

Capabilities:

• Automatic rectangular mesh generation with isoparametric mapping
• Gaussian quadrature (1×1 through 4×4 integration)
• Surface traction and body force loads
• Thermal loading
• Principal stress and strain computation
• Nodal stress averaging (arithmetic, volumetric, and energy-weighted)
• Deformation energy analysis per element

Benchmarks (CSA_2021_BENCHMARKS/)

Validation suite with 10+ progressive frame benchmarks (simple beams through multi-span bridge structures) and multiple ISOP4 test cases across four boundary condition sets.

Documentation

• Frame input format — annotated reference for the frame solver input file
• ISOP4 input format — annotated reference for the ISOP4 solver input file
• Theory and formulation — element formulations, constitutive models, and numerical methods
• Architecture — subroutine call graphs, data flow, and key data structures

Analysis Pipeline

Input (.txt) → GEOMET → SCODE → LOADS → ASSEMB/MKK → SOLVE → STRESS → PLOT
                 │         │       │         │            │        │
             Read mesh   Set BCs  Apply   Assemble     Gaussian  Compute
             & props    & DOFs   loads    K·d = F      elimin.   forces/stress

Building

The source is compiled with the NAG Fortran compiler. Each module includes .make and .mako build files:

cd CSA_2021_FRAME
nagfor -o frame.exe frame.f90

cd CSA_2021_ISOP4
nagfor -o isop4.exe isop4.f90

Usage

Both programs read from a structured text input file and write results to an output file:

./frame.exe < input.txt > output.txt
./isop4.exe < input.txt > output.txt

Input files define: node coordinates, material properties, cross-section data, element connectivity, boundary conditions, and applied loads. See the case-studies/ directories for examples.

How to Run

Frame Example

Using the portal frame benchmark (CSA_2021_BENCHMARKS/case-studies/input_frame_BM_1.txt) — a fixed-fixed portal with a 50 kN/m distributed load on the beam:

cd CSA_2021_BENCHMARKS
./frame.exe < case-studies/input_frame_BM_1.txt > case-studies/output_frame_BM_1.txt

Sample output (nodal displacements and element forces):

 SUMMARY OF RESULTS
 NODAL DISPLACEMENTS
 NODE                    Ux               Uy             Rotz
    1                  0.00             0.00             0.00
    2                  0.00            -0.00            -0.00
    3                 -0.00            -0.00             0.00
    4                  0.00             0.00             0.00

 FORCES AT NODES
 ELEM                    N1               T1               M1               N2               T2               M2
    1           0.15000E+03     -0.33750E+02     -0.45000E+02     -0.15000E+03      0.33750E+02     -0.90000E+02
    2           0.33750E+02      0.15000E+03      0.90000E+02     -0.33750E+02      0.15000E+03     -0.90000E+02
    3           0.15000E+03      0.33750E+02      0.90000E+02     -0.15000E+03     -0.33750E+02      0.45000E+02

ISOP4 Example

Using a single-element plane stress problem:

cd CSA_2021_ISOP4
./isop4.exe < case-studies/input_man.txt > case-studies/output_man.txt

Sample output (displacements, stresses, and energy):

 SUMMARY OF RESULTS
 NODAL DISPLACEMENTS
 NODE                    Ux               Uy
    1           0.00000E+00      0.00000E+00
    2           0.00000E+00      0.00000E+00
    3           0.11062E-04     -0.68653E-05
    4           0.22993E-05      0.50014E-05

 STRESSES(IN CENTER OF GRAVITY) IN ELEMENT:    1
         SIGX                  SIGY                 TAUXY                  SIGZ                  SIG1                  SIG2                 THETA
  0.66194E+01          -0.11587E+02           0.11708E+02           0.00000E+00           0.12347E+02          -0.17314E+02                  0.45

 ENERGY STORED IN THE SYSTEM
             TOTAL VOLUME               TOTAL STRAIN ENERGY             TOTAL STRAIN ENERGY %
                    48.00                       0.89636E-03                            100.00

Output

Results include:

• Nodal displacements (with min/max summary)
• Element internal forces (frame) or stress/strain tensors (ISOP4)
• Principal stresses and directions
• Strain energy and external work balance
• Plot data (PLOT.DAT) for visualization via the MATLAB interface

Tech Stack

Component	Technology
Solver	Fortran 90
Compiler	NAG Fortran (nagfor)
Visualization	MATLAB