Introduction
Structural engineering is an engineering discipline that is concerned with the analysis, design, and testing of structures that must support loads. It is found in many engineering branches, most commonly aerospace, civil, and mechanical engineering. The analysis of structures is necessary to optimize them for their ability to resist loads, to last a lifetime, and to provide a safe engineering solution to oftentimes difficult design problems. The design of structures is critical to the overall process of conceptualizing and producing a product. The testing of structures is usually a final step to assess product fragility and to prove that a specific design meets specified requirements. Structural engineers oversee and participate in all disciplines that are related to the structural engineering of real-world products and structures.

Structural Engineers
Structural engineers have a unique and important responsibility for ensuring that structures are safe, as well as optimized for weight and load bearing capability. The importance of a structural engineer’s abilities and credentials are evident in all walks of life. This can be seen in the design of everyday structures, such as skyscrapers and bridges. It is also obvious in ‘high tech’ aerospace applications, such as airplanes, rockets, or space vehicles, such as the Space Shuttle. Structural engineers routinely provide safe structures that protect people, ensure the safety of astronauts, or simply ‘perform an intended function’. Structural engineers must provide structures that do not fail by overload or fatigue, regardless of the application. The structural engineer works closely with many other disciplines within and outside of engineering.

Education
The educational requirements for structural engineers are very similar to all engineering students. There is a strong emphasis on math skills, with science and the humanities being important secondary skills. Most structural engineers take all the rudimentary classes in statics, dynamics, and strength of materials. In addition, further study in engineering mechanics specialties such as vibration and advanced mechanics of materials is normally emphasized in both Bachelor’s and advanced degree programs. Emphasis on both theoretical and experimental verification of structural behavior is also an important part of the educational process that occurs at structural engineering schools. Once the educational process is completed, graduates can look forward to finding a variety of structural engineering jobs with engineering firms, the government, and private industry.

History
Structural engineering dates back to the days of the pyramids in Egypt. It is obvious that a masterful job of structural design and assembly was done to create these huge structures. These structures were commonly built during this time period because of their stability and the ability for engineers to scale their dimensions for new projects. It is likely that structural theory did not exist at this time, but pyramid designs were based on empirical information that had been gathered from previous successful projects. The Civil Engineering community can look with pride at these historic structures for the engineering ingenuity and resourcefulness in building these massive stone structures.

Introduction
Finite element analysis (FEA) was developed decades ago to solve engineering structural problems. In its infancy, FEA was simply a matrix method to deal with simple structures that could be analyzed with rudimentary computer systems.
However, it has evolved into a widely used method for evaluating a variety of products in many engineering disciplines. FEA has been used for decades to solve complex structural, thermal, and fluid mechanics problems. Applications are typically found in civil and mechanical engineering, but FEA has also been used extensively in electrical engineering as well. Finite element analysis enables engineers to tackle real world complex assemblies and systems that are impossible to solve with simpler methods.

History
The finite element method (FEM) originated in the 1940’s. At this time, there was a need to solve more complex problems in elasticity and structural analysis. As the method evolved, various approaches were recognized that involved dividing a continuous domain into sub domains, or elements. Mathematically, the method involved solving an array of partial differential equations. During the 1950’s, further development of FEA continued in airframe and structural analysis. Research at several universities culminated in more efficient methods for solving the stiffness matrices that were the basis of the method. This research was concentrated in civil engineering applications during the 1960’s, but applications to other engineering disciplines were also beginning to appear at this time. During the late 60’s, three of the more recognized finite element codes were introduced: ANSYS, NASTRAN, and STARDYNE. Advances in computing power and software development over the years have culminated in the efficient, multi-purpose finite element (FE) programs that are available today.

The Finite Element Method
The finite element method consists of three major tasks. The first is pre-processing, where the analyst develops a mesh which consists of nodes and elements. This mesh is the basis for the analysis, and is supplemented with appropriate material properties, element properties, and boundary conditions. The second task is the solution phase, where the elements are assembled into matrices. These matrices are then solved for basic parameters, such as displacements or temperatures. The final step is post-processing, where the analyst checks the results. Part of this process involves reviewing the magnitudes and distributions of the primary solution parameters (such as displacements and stresses).

The Finite Element Model
An FE model consists of a finite number of points (nodes) and elements. The nodes are actually points in space that are used to define the elements. The elements consist of various numbers of nodes (typically from 1 to 20). These elements are defined in space by the location and connectivity of the nodes. Finite elements are actually mini structures themselves, with displacement functions that are defined by the element types. Each element is further defined by element and material properties. The density of the finite element mesh may vary throughout the model, depending on the stress gradients within the structure.

Answers from FE Models
Each node in an FE model is characterized by a specific number of degrees of freedom (DOF). For three dimensional structural problems, the maximum number of DOF is 6 (three translations and three rotations in a global coordinate system). The minimum number of DOF is one (such as temperature for a thermal model). In simple terms, static structural FE models solve the equation F = k x, where F is the applied force, k is the stiffness, and x is the displacement. All of this is done in matrix format, where thousands of DOF are calculated in a single FE model. The most common results from FEA are displacements and stresses. Nonlinear design analyses include large deflection, elastic-plastic deformation, and contact between adjacent structures.