### EXPERT SERVICES — Terms and Definitions

• aspect ratio - the ratio of measurements (length to width, for example) of an element - must be within certain limits to ensure accuracy.
• axisymmetric - element type that can be used to model a solid of revolution. Can only be used when geometry, material, constraints, and loads are all axisymmetric.
• beam element - element whose geometry is defined by a curve, cross-section is input by user as a property.
• bending moment - the torque created by a force applied some distance from the point of concern.
• brick element - type of solid element defined by the volume between six faces (cube shaped). In H-codes, these elements are more accurate than tetrahedral elements. This is not the case for the P-method.
• boundary conditions - the mathematical conditions used to represent the physical restraints on an object (in structural analysis). The conditions are usually dealing with the displacement, stress, or slope at the ends or edges of a member.
• brittle - type of material that exhibits fracture without plastic behavior. Exhibits elastic behavior up until point of failure.
• buckling - a type of structural behavior that exists when a thin object collapses under compression, quickly folding over onto itself. Also known as elastic buckling.
• bulk modulus of elasticity - the ratio of normal stress (tensile or compressive), triaxial and equal in all directions (hydrostatic pressure), to the relative change it produces in volume.
• coefficient of thermal expansion - the amount of strain that a material will undergo when subjected to a unit change in temperature.
• composite shell - common element used to model sandwich composite materials. Material properties may be defined on multiple layers, with different orthotropic properties within each layer. Used often in the aerospace industry.
• contact region - entity that allows for contact between two surfaces. Similar (but better) to gap elements in H-codes.
• conduction - mode of heat transfer that occurs in a solid (like heat through a pot handle).
• constraints - modeling entities that allow for fixing, or restraining a model against movement.
• convection - mode of heat transfer that occurs between a fluid and a solid (like wind blowing over a house).
• convergence - the act of honing in on the correct answer in a numerical simulation. In the H-version of the FEA method, this is manual process of mesh refinement and is achieved by the selective raising (adaptive P-method) of polynomial orders of the approximating equations.
• creep - continuous increase in deformation under constant or decreasing stress. The term is ordinarily used with reference to the behavior of metal under high temperatures.
• damping - the dissipation of energy in a vibrating system
• deformation - deflection that occurs when structural body is under an external load.
• degree-of-freedom (dof) - name given to the freedom of movement for an object in any given direction. Any unconstrained object has six degrees-of-freedom (translation in three directions and rotation in three directions).
• ductility - the ability for a material to become permanently deformed without fracture
• dynamic - a situation that is time-dependent.
• elastic - capable of sustaining stress without permanent deformation. Also used to denote conformity to the law of stress-strain proportionality.
• elements - the simple shapes that a body is broken into for FEA.
• fatigue - the gradual deterioration of a material when subjected to repeated loads.
• finite element analysis - numerical method by which a geometry is broken into a number of simpler shapes, or elements. Governing equations are then formulated on these elements, yielding a number of simple equations. The solution is generally performed using a computer.
• fracture - type of failure exhibited by brittle materials, where there is no deviation from elastic theory until the point of failure.
• gap element - element used in H-codes that allows for contact between two bodies.
• H-method - original version of the finite-element method. Elements are flat-edged and flat-faced, giving faceted representation of geometry. Accuracy is dependent upon mesh size and shape.
• design variables - variables that can be created to aid in testing multiple design variations. Variables can be applied to geometry (dimensions), material properties, etc…
• element - one individual piece used in a finite-element analysis model.
• geometric nonlinearity - type of nonlinearity in structural analysis caused by large deformation. If the geometry changes enough during the course of the analysis, the stiffness will also change (even if the material property does not). Imagine a thin piece of sheet metal. It may stay within the linear range of the material property, but still show a large deflection. This results in nonlinearity because the stiffness (which is a function of both material and geometry), changes during the simulation.
• homogeneous - a material whose properties are the same at any location.
• Hooke's law - stress on a solid is proportional to the strain.
• isotropic - having material properties that do not vary with direction.
• loads - in structural analysis, these are applied to the model to represent any external forces that are acting on the structure.
• material nonlinearity - type of nonlinearity in structural analysis caused by nonlinear relationship between stress and strain for the material used. The material property (Young's Modulus) changes over the course of the analysis, and cannot be input as one number. This can be caused by a material (such as a metal) being loaded above it's yield stress value. It can also be caused by a material that has an inherently nonlinear stress-strain curve. This nonlinearity requires an iterative solution (performed in many steps).
• material properties - these are numbers, entered by the user, that help to define the analysis model. They characterize the material used in the model.
• matrix algebra - a branch of mathematics where groups of numbers arranged in columns and rows are used to perform solutions on large numbers of equations, simultaneously.
• mesh - collection of finite-elements that together represent a geometric body for FEA.
• mid-plane compression - the act of transforming a thin-walled solid CAD model into a surface model, located at the mid-plane of the solid, ready for shell meshing.
• modal analysis - type of analysis that calculates a structure's natural frequencies and associated mode shapes (shapes of the deflection for each mode).
• modulus of elasticity (young's modulus) - the rate of change of stress with respect to strain for the uniaxial stress condition of a material within the proportional limit. Determined using tension test.
• moment of inertia - the integral sum of the all elements of an area multiplied by each elements' distance from an axis. Used in dynamic and beam stress calculations.
• natural frequency - the frequency that a structure will naturally tend to vibrate at when excited by external dynamic loads.
• nonlinear - term used to describe a function whose slope is not constant. The graph of such a function is not a straight line. In structural analysis, used to describe a problem where the relationship between load and deflection is not constant. This usually occurs when the stiffness (K) of the structure changes over the course of the simulation. The problem must usually be solved in an iterative fashion, updating the stiffness along the way. Nonlinearity is common in contact problems, problems with certain materials, and problems with large deflections.
• optimization - design study where software defines the best design attributes.
• orthotropic - term used to denote material properties that vary with direction.
• plasticity - the phenomenon of sustaining permanent deformation without rupture.
• Poisson's ratio - the ratio of lateral strain to longitudinal strain.
• P-method - polynomial-based version of the finite-element method. Elements are geometrically represented by polynomials (curved edges and faces) to more accurately represent the geometry. Accuracy is not dependent upon element size and shape, because convergence is achieved automatically.
• principal stresses - stresses through any point in three principal directions, in which the stress is purely normal (tension and compression only). The values are determined, basically, by rotation of the axes defining the coordinate system.
• radiation - mode of heat transfer that occurs via electromagnetic waves (sun's heat).
• sensitivity - design study where multiple solutions are performed for a problem, each using a variation on the model. Results are graphs that illustrate which design variables are important.
• shear modulus - the rate of change of shear stress with respect to pure shear strain. Variable symbol G. May be determined by using a torsion test.
• shell element - element whose geometry is defined by a surface, thickness is a user-defined property, good for thin-walled structures.
• solid element - element whose geometry is defined by a volume.
• static - type of analysis where time is not a factor in the process. Important quantities do not change over time.
• strain - stretching of material that causes deflection, represented as a percentage of size
• strain energy - mechanical energy stored in a stressed material. This implies stresses within the elastic limit, so strain energy is equal to the amount of work done by external forces in producing the stress.
• stress - measure of force per area, used to predict failure for a given material
• stress concentration - stresses seen due to irregularities of form such as holes, threads, notches, sharp corners. Often the values are calculated using a factor approach.
• symmetry - term used to describe using part of the geometry of a model (1/2, 1/4, etc.) to simulate a situation that is equal on either side of an imaginary plane. Special boundary conditions are required along the symmetry planes.
• tetrahedral element - solid element defined by the volume between four faces (pyramid-shaped). In H-codes, these elements are generally not as accurate as brick elements. They are widely used, however, because automatic meshing schemes create tetrahedrals more easily than bricks.
• thermal analysis - analysis used to determine temperature distributions.
• torsion - load that tends to twist a member, rather than bend or elongate it.
• transient - situation where time is a factor in the process. Important quantities change over time. The term dynamic is very similar, and often used interchangeably.
• ultimate strength - the maximum tensile, compressive, or shear stress that a material can sustain. It is implied that the stress be purely tensile, compressive, or shear.
• two-dimensional element - element whose geometry is defined by a 2-d area. Can be used for linearly extruded cross-section solids or axisymmetric solids of revolution. Only valid if geometry, loads, and boundary conditions are symmetric.
• von Mises stress - the resultant stress from von Mises theory, also known as the distortion energy theory. Assumes yielding can occur in a general 3-d state of stress when the root mean square of the difference of the principal stresses equal tension yield stress.
• yield stress - the stress at which a material exhibits permanent deformation. This is usually determined by measuring departure from the linear stress-strain curve.
• Young's modulus - the ratio of stress with strain, also called the modulus of elasticity.

We hope this glossary was a help to you. If you need information concerning specific terms not included in this list, or wish to submit additional terms for inclusion, please email your questions and comments to info@istllc.com. Thank you.

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