Influence lines are indispensable tools for visualizing and analyzing the dynamic variations in force factors induced by external loads within structural systems. Among these methods, the energetic approach stands as a widely employed technique, rooted in the fundamental principle of work done by changing forces. It enables engineers to transform intricate structural analysis problems into manageable ones by exploring the first derivatives of the radius vector, which represent infinitesimal velocity or displacement. This methodology seamlessly interweaves concepts such as carrier motion, relative motion, and the construction of mechanisms, bringing fresh perspectives to the analysis of influence lines. In this article, we explore the nuances of these novel methods within the domain of mechanism theory. Through comprehensive elaboration and analysis, we elucidate the underlying principles and practical applications of Jacobian contours. Crucially, we introduce a straightforward, rapid, and programmable approach, promising to revolutionize influence line determination in structural engineering. This method bridges the gap between theory and practice, offering the potential to elevate the accuracy, efficiency, and adaptability of influence line analysis. As such, it represents a significant advancement in the field of structural and applied mechanics, with broad-reaching implications for engineering practice.

The energy crisis is currently a major topic in scientific and managerial discussions in the building and construction industry. While employing low-cost strategies for reducing energy usage is beneficial for principals and decision-makers, the primary purpose of this study is to recommend the use of phase change materials (PCM) to improve cooling and heating load management in buildings. In order to accomplish this, the study applies design-builder simulations to a developing country case study. The results indicate that integrating PCM in buildings can reduce energy usage by around 6 percent. Although this value may be lower than other techniques, it is nevertheless important for reaching green building goals in both developed and developing nations. The case study, which takes place in a four-season region, demonstrates the significant potential of the PCM system for both cooling and heating energy management. In addition, the reciprocal performance improvement of PCMs is a remarkable characteristic, especially when contrasted to some conventional systems that focus on a single energy management objective in buildings. Lastly, it should be underlined that the suggested platform is consistent with Sustainable Development Goal 7 (Affordable and Clean Energy Targets).