COMPUTER MODELING OF THE STRESS-STRAIN STATE OF SMALL ARCHITECTURAL FORMS AND TECHNICAL PRODUCTS BASED ON THE FINITE ELEMENT METHOD
Authors:
1.
Kazan State University of Architecture and Engineering
2.
Kazan State University of Architecture and Engineering
3.
Kazan State University of Architecture and Engineering
Type:
Article
Pages:
from 139
to 145
Status:
Published
Received:
07.08.2025
Accepted:
07.08.2025
Published:
07.08.2025
Language:
Russian
Keywords:
FINITE ELEMENT METHOD (FEM), STRESS ANALYSIS, DEFORMATIONS, STIFFNESS MATRIX, PARAMETRIC MODELING, COMPUTATIONAL DESIGN, ROBOTIC MANUFACTURING, GRASSHOPPER, ALGORITHMIC DESIGN, NUMERICAL SIMULATION, ELEMENT APPROXIMATION, CHOLESKY DECOMPOSITION, LDLT DECOMPOSITION, SOFTWARE INTEROPERABILITY, OPTIMIZATION OF ARCHITECTURAL FORMS
Abstract (English):
This article presents the results of computer simulations for stress-strain analysis of small architectural forms (SAF) and technical products using the finite element method (FEM). The primary focus is on algorithmic aspects of stiffness matrix assembly, solving systems of equations, and the impact of modern computational technologies on the design process of complex architectural structures. Key issues related to the approximation of surface elements using linear constraints are discussed, which improves analysis accuracy for objects with complex geometry. The importance of this methodology stems from the need for efficient integration of various mathematical methods to develop precise and stable computational algorithms. The significance of an interdisciplinary approach is emphasized, encompassing computational mechanics, architectural design, and robotic manufacturing. Modern design technologies require comprehensive analysis that bridges multiple scientific disciplines, leading to more sustainable, cost-effective, and functional architectural solutions. The article provides a detailed analysis of FEM algorithm implementation in the Grasshopper environment, demonstrating the connection between parametric modeling and engineering analysis. Special attention is given to numerical methods for optimizing computational processes, enhancing the prediction accuracy of mechanical properties of structures. Optimization, in turn, improves digital design workflows and reduces time costs, which is crucial in contemporary architectural practice. Additionally, the article explores the application of advanced FEM algorithms for analyzing complex architectural structures, including curved elements and anisotropic materials. The proposed methods involve detailed stress-strain analysis, mathematical modeling of load redistribution, and numerical solutions of corresponding equation systems. Case studies demonstrate the effectiveness of these algorithms and their potential integration into modern CAD/CAE systems. The discussed modeling and computational techniques are essential for modern architectural engineering, as they enable the design of stable and optimized structures while accounting for geometric complexity and material properties. The advancement of computational technologies continues to transform design approaches, creating new opportunities for automated analysis systems and digital fabrication. Thus, the research approach presented in this article highlights the necessity of further integrating algorithmic design and computational mechanics to develop more advanced architectural solutions.
This article presents the results of computer simulations for stress-strain analysis of small architectural forms (SAF) and technical products using the finite element method (FEM). The primary focus is on algorithmic aspects of stiffness matrix assembly, solving systems of equations, and the impact of modern computational technologies on the design process of complex architectural structures. Key issues related to the approximation of surface elements using linear constraints are discussed, which improves analysis accuracy for objects with complex geometry. The importance of this methodology stems from the need for efficient integration of various mathematical methods to develop precise and stable computational algorithms. The significance of an interdisciplinary approach is emphasized, encompassing computational mechanics, architectural design, and robotic manufacturing. Modern design technologies require comprehensive analysis that bridges multiple scientific disciplines, leading to more sustainable, cost-effective, and functional architectural solutions. The article provides a detailed analysis of FEM algorithm implementation in the Grasshopper environment, demonstrating the connection between parametric modeling and engineering analysis. Special attention is given to numerical methods for optimizing computational processes, enhancing the prediction accuracy of mechanical properties of structures. Optimization, in turn, improves digital design workflows and reduces time costs, which is crucial in contemporary architectural practice. Additionally, the article explores the application of advanced FEM algorithms for analyzing complex architectural structures, including curved elements and anisotropic materials. The proposed methods involve detailed stress-strain analysis, mathematical modeling of load redistribution, and numerical solutions of corresponding equation systems. Case studies demonstrate the effectiveness of these algorithms and their potential integration into modern CAD/CAE systems. The discussed modeling and computational techniques are essential for modern architectural engineering, as they enable the design of stable and optimized structures while accounting for geometric complexity and material properties. The advancement of computational technologies continues to transform design approaches, creating new opportunities for automated analysis systems and digital fabrication. Thus, the research approach presented in this article highlights the necessity of further integrating algorithmic design and computational mechanics to develop more advanced architectural solutions.
Keywords:
FINITE ELEMENT METHOD (FEM), STRESS ANALYSIS, DEFORMATIONS, STIFFNESS MATRIX, PARAMETRIC MODELING, COMPUTATIONAL DESIGN, ROBOTIC MANUFACTURING, GRASSHOPPER, ALGORITHMIC DESIGN, NUMERICAL SIMULATION, ELEMENT APPROXIMATION, CHOLESKY DECOMPOSITION, LDLT DECOMPOSITION, SOFTWARE INTEROPERABILITY, OPTIMIZATION OF ARCHITECTURAL FORMS
FINITE ELEMENT METHOD (FEM), STRESS ANALYSIS, DEFORMATIONS, STIFFNESS MATRIX, PARAMETRIC MODELING, COMPUTATIONAL DESIGN, ROBOTIC MANUFACTURING, GRASSHOPPER, ALGORITHMIC DESIGN, NUMERICAL SIMULATION, ELEMENT APPROXIMATION, CHOLESKY DECOMPOSITION, LDLT DECOMPOSITION, SOFTWARE INTEROPERABILITY, OPTIMIZATION OF ARCHITECTURAL FORMS
