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5: General Stress Analysis

Last updated

Mar 15, 2021
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- 4.4: Laminated Composite Plates
- 5.1: Closed-Form Solutions

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The results presented in earlier modules for trusses, beams, and other simple shapes provide much of the information needed in design of load-bearing structures. However, materials and structural engineers routinely need to estimate stresses and deflections in geometrically more irregular articles. This is the function of stress analysis, by which we mean the collection of theoretical and experimental techniques that goes beyond the direct-analysis approach used up to now. This is a career field in its own right, and these modules will limit themselves to outlining only a few of its principal features.

5.1: Closed-Form Solutions
This page discusses the mechanics of materials with a focus on stress analysis, emphasizing the importance of closed-form solutions for engineers before using computational methods. It highlights the analysis of stress around circular and elliptical holes, noting significant stress concentration factors and implications for structural design, particularly in aircraft fuselages.
5.2: Experimental Solutions
This page discusses experimental stress analysis, focusing on methods for measuring strain in complex geometries using techniques like strain gauges, photoelasticity, and moire methods. Strain gauges, enhanced by Wheatstone bridge circuits, measure strain at single points, while photoelasticity and moire methods provide full-field strain distributions. Interference fringes indicate strains in materials, with mathematical relationships defined for strain analysis.
5.3: Finite Element Analysis
This page outlines finite element analysis (FEA) as a key engineering method, detailing its processes, including preprocessing, analysis, and postprocessing, particularly in truss structures. It discusses assembling stiffness matrices and the efficient mapping of local to global degrees of freedom. The page also covers calculations involving displacements, forces, and stresses, utilizing software tools, and highlights the importance of numerical integration techniques.
5.4: Linear Viscoelasticity
This page presents an overview of linear viscoelasticity, detailing the mechanical response of polymers and composites, including molecular mechanisms like entropic elasticity and the impact of the glass transition temperature (Tg). It includes discussions on creep compliance, stress relaxation, and models like the Maxwell and Standard Linear Solid (SLS) models, emphasizing stress-strain relationships.

Thumbnail: Example results of Finite Element Analysis computational simulation of a generic superelastic nitinol stent. Open Stent Design, developed by Confluent Medical Technologies (formerly Nitinol Devices and Components, NDC). Analysis by Karthikeyan Senthilnathan, Abaqus Standard from DS Simulia. OSS-Crimp-FEA-08. (CC BY 2.0 Generic; Craig Bonsignore via Flickr)

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