The extensive review of matrix transformation assembly presents the development of PyTruss3D using the direct stiffness method (DSM), which was validated using the commercial software STAAD.Pro. Grounded in the DSM theory, the global stiffness matrices across five different representative models (ranging from simple to complex structures, such as lattice transmission towers to arched roofs) were formulated from the local elements' stiffness matrices. Prevalently, the program calculates the nodal/joint displacements and axial forces and visualizes deformations while storing the generated matrices. Analyzing the robustness and reliability of the program, the results produced were statistically compared with those from STAAD.Pro using the performance measures Root Mean Square Error (RMSE), correlation coefficient (r), and coefficient of determination (R2). The statistical comparison yielded excellent agreement with an RMSE below 0.01 and R2 greater than 0.99 for displacement, and r values ranging from 0.9998 to 1.0 for axial forces. Moreover, PyTruss3D displacement contours replicate the same deformation profiles produced by STAAD.Pro. Slightly robust estimations were observed in the results of the developed program, providing conservative values yet consistent performance. These findings further demonstrate that PyTruss3D can accurately and reliably perform finite element analysis of space trusses, serving as an alternative open-source program for educational purposes (SDG 4) and structural design validation (SDG 9), as well as for future research.
Ledesma et al. (Fri,) studied this question.