# Glossary

## 1D elements

Beam, Bar, Tie, Strut, Spring, Damper, Link and Cable are all 1D elements.

## 2D elements

Quad 4, Quad 8, Triangle 3 and Triangle 6 are all 2D elements.

## 3D elements

Brick 8, Wedge 6, Pyramid 5, Tetra 4

## AASHTO

Acronym for “American Association of State Highway and Transportation Officials”.

## Alignment

An alignment defines a line in space, relative to a grid plane, from which lanes tracks or vehicle are positioned.

## Analysis layer

The analysis layer is a view of elements in a Graphic View.

## Applied displacement

A degree of freedom where the displacement is known at the beginning of the analysis, rather than being solved for.

## Axes triad

Axis sets are displayed in Graphic Views as colour coded triads. The red, green and blue lines represent the x, y and z axes respectively.

## Bandwidth

The width of array required to store a matrix clustered around the diagonal, with the diagonal elements along the first column. A small bandwidth will be more efficient in the storage required.

## Bar element

A particular type of finite element used to model elements designed to take only axial load, e.g. truss members.

## Beam element

A particular type of finite element used to model beam, column and bracing structural elements. GSA uses a linear beam element with 2 nodes.

## Beta angle

The angle used to define the orientation of beam elements in space and the local axis directions of 2D elements. Also called Orientation angle.

## Buckling analysis

An analysis to determine the buckling response of a structure. This can be either an eigenvalue analysis for linear structures or a nonlinear buckling analysis.

## Cable element

Cable elements are primarily used in fabric analysis. Cables are similar to tie elements but are defined by a stiffness and mass per unit length, rather than a cross section.

## Click

Clicking is the action of pressing and immediately releasing the left mouse button.

## Coincident nodes

Coincident nodes are two or mode nodes that are positioned within a defined distance of each other.

## Collapsing coincident nodes

Collapsing coincident nodes is the operation that results in all but the lowest numbered node in a set of coincident nodes to be deleted and all references to these deleted nodes to be changed to references to the remaining node.

## Constraint

A constraint on a degree of freedom, such as an applied displacement, rigid link, repeat freedom or restraint.

## Current grid

A reference to a grid plane. Coordinates are defined and reported in the current grid axes. The grid drawn in Graphic Views is defined by the grid layout of the current grid.

## Cycle

This is a single time step in the dynamic relaxation solution process. During a cycle the model is assumed to be a set of linked nodal masses accelerating through space. At the end of each cycle the position, velocity and forces acting on the nodes are calculated, the resulting accelerations calculated, and the process repeated.

## Degree of freedom

A freedom of a node to move in a particular direction this may be either a translational or rotational direction.

## Design layer

The design layer is a view of members in a Graphic View.

## Diagonal array

An array which has non-zero elements only on the diagonal.

## Direction cosine array

The array relating local and global coordinate system, and used to transform vectors and tensors between different coordinate systems.

## Displacement vector

The calculated displacements at all the degrees of freedom in the structure.

## Drag

Dragging is the action of pressing the left mouse button down and moving the mouse before releasing the mouse button.

## Dummy element

An element that has its dummy attribute set. Dummy elements are ignored during analysis. Certain results can be output for dummy elements.

## Dynamic analysis

An analysis to determine the dynamic response of a structure. A modal analysis gives the dynamic characteristics of the structure while a time-history analysis or response spectrum analysis gives the structural response.

## Eigenvalue

Part of the solution of an eigenproblem. A dynamic analysis is an example of an eigenproblem and the natural frequencies correspond to the eigenvalues.

## Element

An element is an entity that is analysed. An analysis model is made up of elements.

## Engineering scale

An engineering scale is a scale of 1, 1.25, 2, 2.5 or 5 multiplied by a power of 10.

## Entity

A node, element or member.

## Eye distance

The eye distance in a Graphic View is the distance from the eye point to the object point.

## Eye point

The eye point in a Graphic View is the position from which the model is being viewed.

## Finite element

A mathematical representation of a piece of the structure located by nodes and contributing to the stiffness/inertia of the structure.

## Finite element method

The method for analysis of structure by dividing the structure into a collection of connected finite elements.

## Force vector

The collection of forces applied to an element or to the structure as a whole. Normally the force vector for the structure is known and we wish to calculate the displacements. Once the displacements at the nodes are calculated we then want to calculate the internal forces in the elements.

## Form-finding

A process by which the natural shape of a fabric structure is established.

## Full image

The full image is a Graphic View image that displays all aspects of the currently specified view.

## Gaussian elimination

A method for solving large systems of linear equations by successively removing degrees of freedom.

## Generic bar elements

Bars, ties and struts are all generic bar elements.

## Geometric stiffness

The additional stiffness of an element that results from the load in the element.

## Ghost image

The ghost image is a Graphic View image that displays a cuboid representing the global extents of the image. A triad representing the global directions is drawn at the object point. A dashed triad is drawn at the mid-point of the view.

## Global axes

The global axes are the axis set to which all other axes relate. The datum axis set for the model.

## Grid axes

The axes referred to by a grid plane. Commonly used to refer to the axes of the current grid.

## Grid layout

Defines the distribution of grid points or grid lines as drawn in Graphic Views.

## Grid plane

A grid plane is a way of defining a plane for loading etc by reference to an axis set and elevation.

## Grid structure

A Grid structure is one modelled in the global XY (horizontal) plane. Global restraints are applied to the model to force it to deform only in the Z direction.

## Hourglassing

Hourglassing arises with under-integrated elements where there are insufficient stiffness terms to fully represent the stiffness of the element and is noticeable in the results by an hourglass pattern in the mesh.

## Increment

Used in nonlinear, GsRelax analysis to define a single load stage. An increment represents the total imposed loads that are deemed to be present at the time of analysis. It is equivalent to an analysis case generated internally by the GsRelax Solver. For example with single increment analysis a single analysis case is created and all loads are applied at the start of analysis. Whereas with a 2-stage multiple increment analysis, the first increment could be an analysis case with half the load applied and the second increment is an analysis case with the total load applied.

## Inertia matrix

Same as mass matrix.

## Influence analysis

An analysis that calculates the effect at a point due to load at a series of points along the structure.

## Joint

A joint is a constraint which links two nodes together in specified directions and is used for modelling features such as pinned connections.

## Lagrange multiplier method

A technique that is used to impose constraints on a model; in particular applied displacements.

## Legend

The legend is the panel of information that describes the content of a Graphic View. The legend may be displayed either on the Graphic View or in a message box.

## Linear element

A finite element with a low order shape function and no mid-side nodes.

## Linear shape function

2-D elements without mid-side nodes interpolate strains linearly between nodes. This can lead to significant stress and strain discontinuities across element boundaries.

## Link element

A link element is a two node element that is rigid in the specified directions, and transfers forces and moments through the structure.

## List field

This is a field that allows the user to enter a list. The syntax of the list is then checked before the field is accepted.

## Lumped mass

A mass (and inertia) at a node. A lumped mass is treated as a one node element.

## Mass matrix

The relationship between force and acceleration in a linear system. In finite element analysis we consider the inertia of the element as represented by the element mass matrix and the inertia of the whole structure as represented by the structure mass matrix.

## Member

A member is an entity that is designed. Typically a member relates to one or more elements.

## Mid-point

The mid-point is a 3D vector used to specify the pan in a Graphic View. The mid-point vector is the position of the mid-point of the picture relative to the object point in picture axes.

## Modal analysis

Modal analysis solves an eigenvalue problem either for a dynamic or buckling analysis of the structure.

## Node

A point in space. Nodes are used to define the location of the elements.

## Normalisation

A way of scaling a vector or matrix. For example the displacement vector for a node can be normalised, producing a displacement magnitude of one at that node.

## Numeric field

A numeric field allows the user to enter a number. Depending on the context this will be either a real number (e.g. a coordinate) or a whole number (e.g. a load case).

## Numeric format

The format used for the display of numbers. The choice is engineering, to a number of significant figures, decimal, to a number of decimal places, or scientific, to a number of significant figures.

## Numeric/percentage field

This is a field that allows the user to enter either a number or a percentage. These fields are used to allow the user to specify position in either an absolute sense (number e.g. 0.25) or a relative sense (percentage e.g. 10%).

## Object point

The object point is the point about which rotations occur in a Graphic View. Also, in perspective views the position of the eye is measured from the object point.

## Object to eye distance

See eye distance.

## Orientation angle

The angle used to define the orientation of beam elements in space and the local axis directions of 2D elements.

## Orientation axes

The axes about which orientations occur in Graphic Views.

## Orientation node

The node used to define the xy-plane for orientation of beam elements.

## Panel

A panel is an area bounded by beam elements.

## Path

A path is the line across a structure followed by a lane, track or vehicle.

## Picture axes

The picture axes in a Graphic View are x, left to right, y upwards and z out of the plane of the picture.

## Plane structure

A Plane structure is one modelled in the global XZ (vertical) plane. Global restraints are applied to the model to force it to deform only in the XZ plane.

## Prescribed displacement

See “Applied displacement” and “Settlement”.

## Quad element

A linear or quadratic element used in two dimensional analyses with 4 sides and 4 or 8 nodes defining the element.

## Quadratic element

A finite element with a higher order shape function – usually with mid-side nodes.

## Quadratic shape function

2D elements with mid-side nodes (quad8 and tri6) interpolate strains using a fitted quadratic function. This provides more realistic stresses and strains than elements with linear shape functions.

## Reaction

Force which is generated at restraint.

## Restraint

A degree of freedom that is fixed so that it is no longer free. Special cases of restraints are pins and encastré supports. (See also: Member Restraint and Restraint Property.)

## Section definition axes

The axis system used for defining beam sections.

## Selection field

This is a field that allows the user to choose from a list of options.

## Selection/numeric field

This is a field that allows the user to either choose from a list of options or enter a number (e.g. when specifying a material either a standard material can be selected or a user defined material specified).

## Settlement

A degree of freedom which is restrained and given a fixed displacement prior to analysis.

## Shear beam

A particular type of finite element similar to a beam element but taking account of shear deformations.

## Skyline array

A storage scheme which only holds the entries in the stiffness or mass matrix which are on and above the diagonal. Its name derives from the outline of the array elements that are stored.

## Space structure

A Space structure is one that may be modelled in 3 dimensions.

## Spacer element

A spacer element is used to control the mesh during a form-finding analysis.

## Spring element

An element which is defined by stiffnesses in each of the translational and rotational directions. Used to model springs and features such as elastic supports.

## Static analysis

A static analysis loads at how the structure responds to loads which do not vary with time.

## Stiffness matrix

The relationship between force and displacement in a linear system. In finite element analysis we consider the stiffness of the element as represented by the element stiffness matrix and the stiffness of the whole structure as represented by the structure stiffness matrix.

## Structure scale

The structure scale is the scale at which the structure is drawn in a Graphic View.

## Strut element

A strut element is similar to a bar element in that it has axial stiffness only, but will only take compressive forces. Note that since this is a nonlinear element, post-analysis combining of results is inappropriate.

## Subspace iteration

A technique for solving for eigenvalues and eigenvectors iteration of large systems, by projecting the system of equations on to a smaller “subspace”.

## Text field

A text field allows the user to enter a string of text and is normally used for names.

## Thread

Threads are a way for a computer program to fork (or split) itself into two or more simultaneously running tasks.

## Tie element

A tie element is similar to a bar element in that it has axial stiffness only, but will only take tensile forces. Note that since this is a nonlinear element, post-analysis combining of results is inappropriate.

## Topology

The list of nodes which define an element or member.

## Torce lines

Torce lines are generalised thrust lines for two or three dimensions. In 2D (plane frame analysis) they are synonymous with thrust lines (i.e. they show the line of action of axial load) but in three dimensions they can contain both torque and force components, hence the name.

## Tree control

A tree control is a standard Windows control that offers options via expandable branches. Click on the “+” to expand a branch and on the “−” to collapse the branch. Double click on an item to invoke that item.

Sometimes multiple selection of items is possible. This is achieved by holding the control key down to continue selection or the shift key to include all items between the currently selected and the item Shft-Clicked.

## Triangular element

A linear or quadratic element used in two dimensional analyses with 3 sides and 3 or 6 nodes defining the element.

## Unattached node

An unattached node is one that is not referenced in the topology list of an element.

## Variable UDL

A variable UDL is a uniformly distributed load whose intensity varies depending on the loaded length. This is used in bridge analysis.

## Vehicle

A vehicle is defined as a list of axle positions and loadings along with an overall width for use in bridge analyses.

## VUDL

See Variable UDL.

## Wireframe image

The wireframe image is a Graphic View image that represents 1D elements as lines and 2D elements as outlines and displays nothing else, regardless of the current settings for the view.

## X elevation axes

The X elevation axis set is a standard axis set that has its xy plane in the global YZ plane.

## Y elevation axes

The Y elevation axis set is a standard axis set that has its xy plane in the global XZ plane.