Introduction - Static, Dynamic, Implicit, and Explicit Methods in FEA
Finite Element Analysis is considered to be one of the fundamental instruments that are used in the functionalities of civil engineering. Civil Engineering is the form of engineering that deals with the formation of roads, tanks, bridges, buildings, and other attributes that define the constructive part of modern life. Urban areas and cities, even townships in contemporary times are having modern constructions of roads, dams, and buildings. Thus this automatically increases the significance of the functionalities of civil engineering and its components, like finite element analysis or FEA. The main aim of FEA is to reduce the complexity of the physical structures that are too difficult for simple analytical techniques, by providing numerical calculations. Finite elements analysis is also used by civil and structural engineers to comprehend the behavior and loopholes of a building or a construction. The method used by FEA is called finite elements method or FEM by which a structural component is dissected into its numerous elements and is materialized by mathematical and algebraic equations for helping the engineers to design or to find loopholes in their construction.
To analyze the structural design, civil engineers use four types of analysis or methodology that fall under the umbrella analysis of FEM. They are ly, “static, dynamic, explicit, and implicit methods” and are used to understand the innumerable structural problems faced by engineers during construction. The concerned assignment has already provided a brief description of FEA in the above section, and the latter half of the assignment aims to address the other components of FEA. The following study will focus on the comparison of the four different elements and their practical applicability in constructional projects by engineers. The study will also aim to trace the computer implementation of FEA for comprehensively summarising the findings.
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Static Analysis is one of the most significant and commonly used methods or analysis techniques in the finite element analysis tool. Static analysis is also known as “static stress analysis” and focuses on the components of structural analysis (Madenci, 2019). This method aims to understand the “stress, deformation, and strain” of a construction “under a range of load conditions” to eliminate any possibilities of construction failures. This process eradicates the possibility of carrying any expensive fault in the construction while it is materializing. This analysis calculates the impact of loads on construction and its immediate impacts, for instance, the linear static analysis is used to comprehend the vulnerability and strength of hydrological projects like dams, and irrigation channels. On the other hand, non-linear static analysis is more complex to formulate but comprehends similar issues like the identification of vulnerability in construction (Madenci, 2019). Dynamic Analysis is described as the strong stimulation method by which difficult and complex engineering problems are solved (Subki et al., 2022 ). This method or analysis benefits the engineers to understand the "impact of the transient loads" and to provide alternative solutions to the vibration issues of construction. Just like static analysis, one can divide dynamic analysis into linear and non-linear analysis (David Müzel et al., 2020).
Both of the elements, that is, the static and dynamic analysis of the finite element analysis or FEA are significant in their rights (Szabó, and Babuška, 2021). However, the study here will aim to provide a comparative analysis of static and dynamic methods of FEA, and the similarities and dissimilarities between them will be outlined accordingly. The selection of the methods, that is, of static and dynamic methods is dependent on the engineers who will conduct a finite element test, but there must be a caution for them to understand and accept the different and often opposite results that erupt from the two non-identical analyses. According to the theoretical approach, a static method of analysis can only be applied if the “stimulated system does not depend on time”. Also, the load being a component must be applied evenly, and in a constant manner. However, with the dynamic analysis, both the load and the system might encounter a change in the context of time. Inertia constitutes a significant or fundamental position in the dynamic analysis of FEA, as it can alter the results (Szabó, and Babuška, 2021). In the dynamic analysis, the inertia and the load that is created by the acceleration of the system are considered significant, whereas, the static analysis does not take this matter into account. Not only theoretically, but there are also substantial differences between the two forms of analysis in mathematical calculations found as well (Ursini et al., 2022). In mathematical terms of analysis the static method, the “stiffness matrix” of the finite element analysis tool is solved. Whereas in the dynamic analysis not only the “stiffness matrix” is solved, but the “mass matrix” is solved as well. Another dissimilarity between static and dynamic analysis of the FEA model is that the latter requires more time to predict the analysis of the construction rather than the former. The loads that are considered in the dynamic analysis are either of the time or frequency domain. Both are efficient in finding defects within structures, however, dynamic analysis is considered to identify the failures, and static analysis is used majorly to understand the reason behind such failures.
There are innumerable dissimilarities between the two kinds of analysis that are an offshoot of finite element analysis. They have theoretical and mathematical differences from each other and possess different methodological approaches to solving the issue. However, the most significant issue that makes them both identical to each other and similar is the aim of these analyses. Both analyses have a similar aim to identify the structural defects and loopholes in the design of a construction. This identical aim of the analyses provides contemporary engineers with an upper hand in designing and constructing defect-free and sound-quality buildings. They are complementary to each other and are required by the systems engineers to find the faults and design loopholes in their structure, which in turn will reap a construction that is sound, secure, safe, and qualitative.
The applicability of static and dynamic analysis under the umbrella of FEA has multiple values (Szabó, and Babuška, 2021). By referring to specific structural problems, for instance, the construction of a bridge or building, both analyses can be applied here. The static test analysis is used to understand and investigate the “structural performance and construction quality” of a bridge. Through this analysis, the real ability of the construction site, for instance, a bridge’s capacity to hold loads are investigated. Thus static analysis has the applicability of ensuring the durability and capacity of a constructional structure in progress. The applicability of the dynamic test in FEA is mostly done on railway tracks, which calculates the durability of the same (Wang et al., 2020). Mathematical calculations take into account the “possibility of resonance occurrence” by calculating both the frequency of the train lines and the trains. However, the most significant factor of applying dynamic tests is to ensure the ability of a contribution to withstand environmental hazards like earthquakes, thunderstorms, and floods.
The other two elemental methods that consist of a part of the finite element analysis are the explicit and implicit methods. Usually, there are almost zero to minimal differences between finite element analysis and finite element methods, but there have been subtle differences between the two. The latter is the actual methodical approach by which one can find and investigate structural defects whereas, the former means the context in which the actual calculations take place. The explicit finite element method denotes the specific method used by engineers who calculate the condition of a “given system at a different time from the current time.” This benefits civil engineers in various ways by letting them realize the weak spots, loopholes, and design faults in their structural plans and methods (Garoz et al., 2019). By the explicit method, engineers stimulate artificial phenomena by which they understand the condition of their designs in a more holistic way. Another form of similar method is called the implicit finite element method which solves the issues by calculating “both the present and later states of the given systems”. This method also benefits the engineers to instigate artificial happenings in their construction structures and identify any hazardous and structural flaws present within (Yang, Deng, and Li, 2019).
There are substantial differences between the two methods in the FEM system and the assignment in this section will follow a detailed analysis of the differences between these two factors. However, before coding the differences between the two, the context of the usage of these tools must be understood. Civil engineers mainly use various kinds of software for analysing. Through the explicit methods “new state can be calculated with ease, considering the available data in the current or present state”. Whereas, the implicit method fails to calculate directly a new state from the old state. The implicit method also acts like a solver of the “unknowns in the numerical equations by the inversions of the matrices that produce the models”. The implicit method is often described as time-consuming however, the method only takes a lot of time if the matrices are larger or bigger in numbers, and then automatically the calculations take much more time than usual. The solutions or answers that are received from the implicit calculations are more stable in their temperament and provide an opportunity for more time increments. Just like inertia in the previous section, acceleration forms an important part of the issue of explicit methods here. Thus explicit methods are used for investigating and solving the issues of acceleration. “Acceleration, velocity, and displacement” are a few significant issues in the structural construction of civil engineering, and the explicit method of FEA considers all these issues and solves them accordingly to produce a construction that is free of hazards (Finite Element Analysis FEA, 2023). However, the point of difference between the implicit and explicit in this matter is that the latter does not produce results that are stable like the former. To produce accurate results, much more time is required by the explicit method, as it breaks down the analysis into smaller steps. It is often believed that implicit methods are taken into consideration in most cases to solve the issues due to their greater adaptability to the problems and the stability of the results it bring about, rather than explicit methods. In general words, it can also be put like the implicit methods are usually used to solve simple civil engineering issues, however, a considerate amount of time is required as extensive calculations and methods are being followed. However, with modern technology and quality software, the explicit methods are now not time-consuming and often bring about more stable results than the implicit ones.
Despite the methodological differences present between the implicit and explicit methods of FEA, there are subtle similarities between the two. Both of these methods are deployed or utilized to bring about more or less stable results that will benefit the civil engineers to understand the structural ability of their construction and design. The main aim of these two methods is to provide accurate results to the tests which will benefit the engineers to produce more or less accurate building and construction. The main aim of these two methods can be considered as the similarity between explicit and implicit methods of FEA (Yang, Deng, and Li, 2019). Both these methods have applicability in their functionalities in the civil engineering outlook. The main aim of civil engineering is to produce and construct better quality buildings and structural constructions, and both these methods are used by engineers to understand the fundamental flaws within their systems. Both these systems benefit the engineers as the results that come out of these tests give the engineers a fair idea about the outcomes of their designed buildings and constructions against hazardous problems. The potential results make the engineers apply various other methodological approaches that are aimed either to upgrade the design or to solve any underlying issue that was identified during the process. With the absence of implicit and explicit methods, it would have been extremely difficult for the engineers to look for the fatal flaws within their systems and it would be also bad for the common people’s safety. Thus it can be stated here that the applicability of these two methods for building bridges, and other constructions are essential as it provides a security check for the sustainability of those constructions by eliminating the specific structural problems.
Computer implementation of the Finite element analysis means the methods in which FEA or FEM is carried on by the process as carried on by a computer. The main aim of finite element analysis or finite element method is to understand the behavior of the construction under pressure or load. The methods discussed above usually calculate and analyse the behavioral patterns and changes of the construction against the load and engineers formulate solutions against it. The modern technological advent currently enables to understanding, of structural, fluid, and thermal conditions of the product that is often believed to have “transformed the physical experience of the products”. These are now described as “partial differential equations” or PDEs. The computer implementation of finite element analysis nowadays can calculate these “linear and non-linear PDEs”, which benefits the engineers to produce results that are reaping results that will change the construction for good. The FEA methods like static, dynamic explicit, and implicit methods are all currently used via the help of computer implementation by the engineers as they run tests to identify the vulnerabilities of the construction. There are tests like “structural static analysis” that provide hypothetical analysis of small-scale models and predict the durability of the large-scale ones if constructed. The second through computer implementation is d “thermal engineering analysis” which measures and investigates the variety of impacts of thermal temperatures on constructions and how they modify it. “Modal analysis” enables to understand the ability of a building or a construction’s durability to withstand the frequencies, especially externally originated frequencies (Bahari et al., 2019). This analysis as programmed from computer implementation is helped by various software and benefits the engineers to understand the structural flaws of their constructions. This model might help the engineers to innovate and understand the future situation of their designed building against potential dangers of natural calamity. FEA in current terms is known as the computerized program to predict various fatal and design flaws a construction can carry during its formation. There is various software that is used in the whole process of FEA, as desired above. The software that is used can be d, “MATLAB”, “FREEFEM”, “Ansys Mechanical”, and others are the direct software used by the engineers to bring about the real results of the buildings.
The computer implementation of FEA or FEM has some structural steps likely pre-processing, processing, and post-processing (Foti, and Berto, 2019). This section of the study will analyze the above terms and will also analyze the processing time that is required. “Pre-processing” in finite element analysis denotes the first step in the long process of problem-solving factors. This first step to solve the problem in the finite element analysis is also known as “Meshing”. This process denotes the method of dividing the full project into smaller sections called “elements”, and these smaller sections constitute the foundational base on which “boundary conditions and external effects are specified.” this first step also involves formulating equations for each of the elements, and when all the elements will accumulate it will be easier to identify the problem. Load must be applied in this part of the finite element analysis for accurate results. The second step is called the “processing step” in the finite element analysis model. This step has been considered the most important and fundamentally essential one in the three steps of FEA, as in this step one will find the analysis. The main aim of FEA is to analyze the conditions of the designed building, and the “processing step” provides the analysis (Magomedov, and Sebaeva, 2020). The elements from the previous step are all assembled and analyzed thoroughly. This is an equational approach by which solutions to difficult engineering issues are answered.
The last step is called the “post-processing” step which systematically deals with the ease with which the analyzed data or information brought from the “processing” step is presented. This process requires additional software which will provide the analysis with a presentable outlook. The computer implementation of the “post-processing” step can transform the final results into HTML files, reports, graphic reports, and diagrams by which it will be easier for the systems engineers to visualize the problem for not only themselves but also for others (Pan et al., 2022).
The processing time required by all three steps is different from each other. The “pre-processing” step requires the most amount of time, as the division of the whole structure into different and smaller sections of elements requires time (Foti, and Berto, 2019). The second and third step equally requires quality time as well for properly analyzing the problems and formulating them into standard documents.
Conclusion
The study has followed a detailed analysis of the various aspects of civil engineering. The study has systematically investigated and outlined the issue of finite element analysis. The study also provides the outline of the finite element method by which the analysis takes place. The essay in concern has provided greater outlines of the issues of various principles of FEA or FEM. The study here critically analyses the principles of static and dynamic methods of finite element analysis. The differences between them are highlighted but the similarity between them forms the most significant part. Both are used by the methodical approach for solving and identifying the structural flaws in the designs of constructible buildings. Similarly, the other methods, likely, the implicit and explicit methods were applied and analyzed here. Differences and similarities between these two points were also featured. Along with these principles of methods, their applicability in the constructional factors is also investigated. The study here also focuses on the three most important phases of the FEM process, and the analysis of these three procedures is also followed. The study here emphasizes finite element analysis and its principles and implications on the factors of civil engineering.
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