MATHEMATICAL MODELLING AND STRUCTURAL ANALYSIS IN CIVIL ENGINEERING: A COMPREHENSIVE RESEARCH STUDY ON PREDICTIVE METHODS FOR LOAD DISTRIBUTION, STRESS BEHAVIOUR, AND DESIGN OPTIMISATION

Abstract

This paper introduces a holistic framework, which combines mathematical modelling, finite element simulations, predictive algorithms, and optimisation strategies to assess and enhance structural performance in civil engineering. The methodology involved closed-form solutions of the analytical methods, as well as finite element method (FEM) of beams, frames, and multi-storey structures, with optimisation using genetic algorithms. Findings showed that FEM and analytical predictions were very similar with the difference usually less than 3 percent, which proves the validity of the computational method. The analysis of stress behaviour showed that both reinforced concrete and steel structures were not subjected to excessive stress levels, which indicated good material performance. The efficiency and sustainability benefits were demonstrated by optimisation having reduced structural weight by 12.4% without compromising serviceability and strength requirements. The credibility of the predictive framework was also supported by validation as it was consistent with theoretical models. The results highlight the possibilities of hybrid computational and predictive approaches to improve accuracy, efficiency, and material savings in structural design. The study will help to develop predictive modelling in civil engineering and will be the basis of applying artificial intelligence and uncertainty-based methods in the future.