A STUDY ON THE APPROXIMATE METHODS VS EXACT METHODS OF STRUCTURAL ANALYSIS

The analysis of statically indeterminate structures, using the force and displacement methods, are considered as exact, as in such an analysis, the conformity and equilibrium conditions of the structure are satisfied exactly. However, the results of such a particular analysis represent the particular structural response only to the purpose up to which the model of the structure represents the particular structure. These methods are often reliably used, given as accurate as possible analytical model of the structure is employed within the analysis. But due to the difficulties related to exact analysis like time consuming computations of deflections and finding solutions of multiple equations, further complicated by the relative sizes of the members of the structure, the preliminary designs of indeterminate structures are often supported by the results of approximate analysis. Approximate analysis becomes very convenient to use within the planning phase of projects, when various alternative designs of the structure are considered and compared with reference to economic aspects. This text aims to match the results from the 2 methods obtained with numerical analysis on a frame structure. The approximate methods are expected to yield results within 25% of the precise solutions.

Multidisciplinary Aircraft Conceptual Design Optimization Considering Fidelity Uncertainties

Aircraft conceptual design traditionally utilizes simplified analysis methods and empirical equations to establish the basic layout of new aircraft. Applying optimization methods to aircraft conceptual design may yield solutions that are found to violate constraints when more sophisticated analysis methods are introduced. The designer's confidence that proposed conceptual designs will meet their performance target is limited when conventional optimization approaches are utilized. Therefore, there is a need for an optimization approach that takes into account the uncertainties that arise when traditional analysis methods are used in aircraft conceptual design optimization. This research introduces a new aircraft conceptual design optimization approach that utilizes the concept of Reliability Based Design Optimization (RBDO). RyeMDO, a framework for multi-objective, multi-disciplinary RBDO was developed for this purpose. The performance and effectiveness of the RBDO-MDO approaches implemented in RyeMDO were evaluated to identify the most promising approaches for aircraft conceptual design optimization. Additionally, an approach for quantifying the errors introduced by approximate analysis methods was developed. The approach leverages available historical data to quantify the uncertainties introduced by approximate analysis methods in two engineering case studies: the conceptual design optimization of an aircraft wing box structure and the conceptual design optimization of a commercial aircraft. The case studies were solved with several of the most promising RBDO-MDO integrated approaches. The proposed approach yields more conservative solutions and estimates the risk associated with each solution, enabling designers to reduce the likelihood that conceptual aircraft designs will fail to meet objectives later in the design process.

Multidisciplinary Aircraft Conceptual Design Optimization Considering Fidelity Uncertainties

Aircraft conceptual design traditionally utilizes simplified analysis methods and empirical equations to establish the basic layout of new aircraft. Applying optimization methods to aircraft conceptual design may yield solutions that are found to violate constraints when more sophisticated analysis methods are introduced. The designer's confidence that proposed conceptual designs will meet their performance target is limited when conventional optimization approaches are utilized. Therefore, there is a need for an optimization approach that takes into account the uncertainties that arise when traditional analysis methods are used in aircraft conceptual design optimization. This research introduces a new aircraft conceptual design optimization approach that utilizes the concept of Reliability Based Design Optimization (RBDO). RyeMDO, a framework for multi-objective, multi-disciplinary RBDO was developed for this purpose. The performance and effectiveness of the RBDO-MDO approaches implemented in RyeMDO were evaluated to identify the most promising approaches for aircraft conceptual design optimization. Additionally, an approach for quantifying the errors introduced by approximate analysis methods was developed. The approach leverages available historical data to quantify the uncertainties introduced by approximate analysis methods in two engineering case studies: the conceptual design optimization of an aircraft wing box structure and the conceptual design optimization of a commercial aircraft. The case studies were solved with several of the most promising RBDO-MDO integrated approaches. The proposed approach yields more conservative solutions and estimates the risk associated with each solution, enabling designers to reduce the likelihood that conceptual aircraft designs will fail to meet objectives later in the design process.

Haar Algorithm for The Analysis of Fractional Order Calculus Based Computation Problems Associated With Electromagnetic Waves

This paper proposes a haar algorithm with the phase wise flow for three distinct cases of fractional order calculus-based electromagnetic wave machine problem. The numerical solution to these programming problems was presented in tabular and graphic form using precise, approximate analysis and haar schema for comparative analysis. Convergence research was also carried out to validate the accuracy and efficacy of the system suggested. The proposed scheme is suited for the numerical solution of the addressed type of computational problem due to its uncomplicated and easy-to-implement, professional, fastness and high convergence rate.