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--- wiki:sns:snspro:linear_static_analysis [2017/07/14 13:11] – claire
+++ wiki:sns:snspro:linear_static_analysis [2017/07/14 13:15] (current) – claire
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 Structural analysis aims to predict deformation and stresses in a body (or collection of bodies) that is restrained from moving and is subjected to external forces (loads). Different theoretical models of structural analysis have been developed to simulate a variety of realistic physical behaviors and phenomena. The simplest and the most widely used type of structural analysis is linear static analysis, based on theory of lineary elasticity.
-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.
+Like all numerical simulations methods, Scan&Solve Pro 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.
   *  [[#Mathematical Model: Linear Elasticity|Linear Elasticity]]
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 **Linearity:** Model deformations (displacements) are linearly proportional to applied loads (forces). For example, doubling the magnitude of the force will double the magnitude of the resulting deformations.
-Linear static analysis predicts the magnitude of stresses and elastic displacements within the body. In locations where the magnitude of stresses exceed certain levels, linear static analysis predicts material failure based on several experimentally verified failure criteria. The type of failure depends on the type of material and the stress levels; linear static analysis cannot predict whether failure results in large permanent deformation, cracks, or breakage, but only that the stresses and displacements will exceed the elastic limit of the material.
+Linear static analysis predicts the magnitude of stresses and elastic displacements within the body. In locations where the magnitude of stresses exceed certain levels, linear static analysis predicts material failure based on several experimentally verified [[wiki:sns:snspro:failure_criteria|failure criteria]]. The type of failure depends on the type of material and the stress levels; linear static analysis cannot predict whether failure results in large permanent deformation, cracks, or breakage, but only that the stresses and displacements will exceed the elastic limit of the material.
 ===== Scan&Solve Numerical Model =====
-Scan&Solve™ is a generalized form of the classical Finite Element Analysis (FEA). Classical FEA approximates an idealized theoretical model of physical behavior by breaking up the model or space into small pieces called finite elements. But Scan&Solve™ was developed specifically to liberate FEA from the tyranny of meshing, while preserving most of the advantages of this classical and widely accepted method of engineering analysis. The basic idea is simple: create separate geometric and physical representations of the model in question and combine them only when necessary, without requiring expensive and error-prone data conversions and always using the most authentic representation available. The concept is illustrated below.
+Scan&Solve Pro uses the same core approach as Scan&Solve™ and is a generalized form of the classical Finite Element Analysis (FEA). Classical FEA approximates an idealized theoretical model of physical behavior by breaking up the model or space into small pieces called finite elements. But Scan&Solve™ was developed specifically to liberate FEA from the tyranny of meshing, while preserving most of the advantages of this classical and widely accepted method of engineering analysis. The basic idea is simple: create separate geometric and physical representations of the model in question and combine them only when necessary, without requiring expensive and error-prone data conversions, and always using the most authentic representation available. The concept is illustrated below.
 {{ :wiki:sns:snspro:sns17.jpg?700 |}}\\
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 ===== Physical Reality =====
-It is important to remember that Scan&Solve™ computes a numerical approximation of an idealized theoretical model, not physical reality. Every model has its limitations. For example, the linear theory of elasticity predicts infinite stresses near "wedges", re-entrant corners, interfaces between different materials, and so on. In physical reality, this cannot happen, because the material simply deforms more "plastically" (as opposed to "elastically"). But in the computer simulation, this means that at some points in your model, stresses will never converge – they will just get bigger and bigger as you increase the resolution. The more complex your model is, the more likely you will have some points like that.
+It is important to remember that Scan&Solve Pro, similar to Scan&Solve™, computes a numerical approximation of an idealized theoretical model, not physical reality. Every model has its limitations. For example, the linear theory of elasticity predicts infinite stresses near "wedges", re-entrant corners, interfaces between different materials, and so on. In physical reality, this cannot happen, because the material simply deforms more "plastically" (as opposed to "elastically"). But in the computer simulation, this means that at some points in your model, stresses will never converge – they will just get bigger and bigger as you increase the resolution. The more complex your model is, the more likely you will have some points like that.
-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.
+More generally, the linear static model of elasticity (and hence Scan&Solve Pro) 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:
+Again Scan&Solve Pro similar to 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 experients. 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.