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--- wiki:sns:sns2014:linear_static_analysis [2017/07/12 16:07] – claire
+++ wiki:sns:sns2014:linear_static_analysis [2017/07/13 14:08] (current) – claire
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+~~CLOSETOC~~
+{{TOC:wide}}
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 ====== Linear Static Analysis ======
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 Like all numerical simulations methods, Scan&Solve™ numerically approximates this idealized model of linear elasticity within some limited precision. As such, Scan&Solve™ can provide insight into structural properties of solid shapes and help in choosing the best available alternative. However, numerical simulation of an idealized mathematical model is not a substitute for physical testing and should not be relied upon for critical design decisions.
-  *  [[wiki:sns:sns2014:Linear Elasticity|Linear Elasticity]]
+  *  [[#Mathematical Model: Linear Elasticity|Linear Elasticity]]
-  *  [[wiki:sns:sns2014:Scan&Solve Numerical Model|Scan&Solve Numerical Model]]
+  *  [[#Scan&Solve Numerical Model|Scan&Solve Numerical Model]]
-  *  [[wiki:sns:sns2014:Physical Reality|Physical Reality]]
+  *  [[#Physical Reality|Physical Reality]]
-  *  [[wiki:sns:sns2014:Known Limitations|Known Limitations]]
+  *  [[#Known Limitations&Common Problems|Known Limitations]]
 ===== Mathematical Model: Linear Elasticity =====
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 More generally, the linear static model of elasticity (and hence Scan&Solve™) does not account for many important physical phenomena, including vibration, buckling, material and geometry non-linearities, large and plastic deformations, and so on.
+===== Known Limitations & Common Problems =====
+Scan&Solve computes a [[#scan_solve_numerical_model|numerical approximation]] of a mathematical model of [[#Mathematical Model:linear_elasticity|linear elasticity]]. As is the case with all such software, the computed stresses and displacements should not be confused with [[#physical_reality|physical reality]] and should not be used for critical design decisions in place of physical experiments. A number of factors, briefly described below, can cause Scan&Solve answers to deviate significantly from physical reality:
+  * **Model is not linear elastic.** A linear elastic model of stress is not applicable in many situations, e.g. non-linear material properties, large plastic deformations, vibrations, buckling, thermal stresses, and so on.
+  * **Idealized geometry and material properties.** While geometric inaccuracies may be quantified by design and manufacturing tolerances, predicting the effect of material variability is usually more difficult.
+  * **Imprecise or unrealistic boundary conditions.** The correctness of the model depends critically on the type (are they really static?) and accuracy of restraints and loads. But these parameters are rarely known precisely, and are sometimes simplified or idealized, contributing to uncertainty of the computed results. For example, edge restraints are non-physical idealizations of small-face restraints; their use may result in poor solutions in the vicinity of such edges.
+  * **Low resolution.** Every known stress analysis approach (including Scan&Solve) relies on spatial discretization of the geometry in one way or another. Scan&Solve is unique because it uses volumetric discretization of space that does not conform to geometry, and the user does not need to deal with meshing, but fundamentally, it still relies on the notion of a "finite element" which is associated with some volumetric portion of geometry. It is usually impossible to estimate a priori how many elements are sufficient for accurate answers. Scan&Solve currently does not perform any posteriori analysis of the computed solutions for accuracy or convergence.
+  * **Missed small features.** Scan&Solve tolerates small imperfections and features in the noisy or overly detailed boundary representation of a solid. However, this means that at low resolution, it could also miss some important features, such as small holes, gaps, and channels that could affect accuracy or correctness of computed solutions.
+  * **Large size to scale ratio.** The size to scale ratio is a fundamental barrier of all numerical methods, and not a limitation unique to Scan&Solve. Challenging models include thin-walled solids, slender truss-like structures, solids restrained on very small faces, and other models where the ratio of the overall size of the solid to the smallest dimension %%('%%scale') on the object is very large. Accurate analysis requires that the size of finite element should be small enough to resolve the smallest scale of the mode. But if the model is also very large, this will result in a huge number of elements, easily exceeding the maximum resolution available in Scan&Solve.
+  * **No adaptive analysis.** Some of the above problem may be alleviated by varying the size of the elements throughout the space, depending on the size of small features and/or desired resolution. The current version of Scan&Solve does not support such adaptive analysis.
+  * **No point restraints.** Only surface areas and edges can be restrained in the current version of Scan&Solve, as dictated by the theory. Point restraints are commonly used in mesh-based FEA packages where they are applied to nodes. But such restraints are actually not physical and may result in poor solutions in the vicinity of the restraints. Although edges can be restrained, please remember that they are also non-physical idealizations of small-face restraints. Using edge restraints may result in poor solutions in the vicinities of the restrained edges.
+  * **First degree numerical approximation.** The current version of Scan&Solve relies on first degree (linear) polynomial functions (splines) to approximate the solution. Some structural analysis problems require higher-degree functions to achieve accuracy and convergence. We expect future versions of Scan&Solve to support such functions.