Components of a structure not of direct interest but they may have some influence of the behaviour of the part of the structure that is of interest (the primary component) and have to be included in the analysis in some approximate form.
A form of matrix products that preserves symmetry of equations. The product A x B x A(transpose) is self-adjoint if the matrix B is symmetric. The result of the product will be symmetric for any form of A that is of a size compatible with B. This form of equation occurs regularly within the finite element method. Typically it means that for a structural analysis the stiffness (and mass) matrices for any element or element assembly will be symmetric.
Occurs in cyclic loading where the plastic strain in each cycle stabilises so that the total strain within a cycle is less than twice the yield strain (the strain when the stress reaches the yield stress).
Ways of defining an element’s shape, with particular reference to how the shape differs from the theoretically perfect shape for that element type. Parameters include Aspect Ratios, taper, skew, curvature, warpage and variation of the Jacobian.
The phenomena which occurs when thick elements give overstiff results when modelling thin beams/plates/shells, due to an excess of shear energy being present. It can also affect 2D and 3D continuum elements.
Used to describe a software environment providing Simulation Data Management functionality, either built on a dedicated Simulation Data Management platform, a Product Lifecycle Management platform or elsewhere.
A PDM system which has been extended to enable the management of some simulation data items and simple simulation datasets which are usually created within CAD-embedded simulation applications by Design or Manufacturing Engineers.
A strategy of pro-active management of simulation activities to ensure professional working practices, assure the organisation's confidence in simulation results, and build and nurture modelling and simulation capabilities.
A measure of the angular distortion arising between two vectors that are at right angles in the basis space when these are mapped to the real coordinate space. If this angle approaches zero the element becomes ill- conditioned.
A situation that occurs when a vertical line in the load-displacement curve is encountered, and two or more equilibrium states are possible for the same applied load. Also referred to as Snap Through Buckling.
A situation that occurs when a vertical line in the load-displacement curve is encountered, and two or more equilibrium states are possible for the same applied load. Also referred to as Snap Back Buckling.
The accuracy of the solution of the equations used in the finite element method, usually referring to the main stiffness equations. When a very large number of variables exist or the model generated is poor, accuracy can be lost due to ill-conditioning arising from the numerical processes.
An indication of the efficiency of the solution of the equations used in the finite element method, usually referring to the main stiffness equations. Minimising the number of such equations without compromising solution accuracy is a common challenge.
Solution methods that exploit the sparse nature of finite element equations. Such methods include the Frontal Solution and Cholesky (skyline) factorisation for direct solutions, conjugate gradient methods for iterative solutions and the Lanczos method and subspace iteration (simultaneous vector iteration) for eigenvalue solutions.
The Fourier transform of the correlation function. In random vibrations it gives a measure of the significant frequency content in a system. White Noise has a constant spectral density for all frequencies.
A series of computer readable data models which form an international standard for exchange of product definition data, relevant to finite elements as a medium for data transfer to and from CAD packages. It is planned to eventually replace the existing standards such as IGES, SET and VDA-FS.
For a hypothetically small increase in crack length or area, this is the amount of strain energy released divided by that length or area. It equals the negative of the Potential Energy Release Rate when elastic conditions predominate.
Used in analysing creep behaviour under variable load where the creep strain rate is assumed to depend on the current stress and accumulated creep strain, or in plasticity where the current yield stress is a function of the plastic strain.
A local area of the structure where the stresses are significantly higher than the general stress level. A fine mesh of elements is required in such regions if accurate estimates of the stress concentration values are required.
Lines along which the stresses are discontinous. If the geometry or loading changes abruptly along a line then the true stress can be discontinous. In a finite element solution the element assumptions means that the stresses will generally be discontinuous across element boundaries. See also Stress Error Estimates.
In a finite element solution the element assumptions means that the stresses will generally be discontinuous across element boundaries. The degree of discontinuity can then be used to form an estimate of the error in the stress within the finite element calculation. See also Stress Discontinuities.
A fracture parameter at a crack tip when under conditions of Linear Elastic Fracture Mechanics (LEFM). It is a function of applied load and crack length, suitably dimensioned to have a finite value at the tip even though the stresses are singular there, and may be used to characterise the state of fracture there.
The components of stress (strain) written in tensor form. For a general three dimensional body this forms a (3x3) matrix with the direct terms down the diagonal and the shear terms as the off-diagonals. See also Stress / Strain Vector.
The material property behaviour relating stress to strain. For a linear behaviour this is Hookes law (linear elasticity). For elastic plastic behaviour it is a combination of Hookes law and the Prandtl-Reuss equations.
A mesh modelling technique whereby a part of a structure, containing a number of elements, can be stored by the software as a single element. It can then be used for a variety of different purposes, just as if it were a new element type with its own stiffness matrix.
Substructuring is a form of equation solution method where the structure is split into a series of smaller structures - the substructures. These are solved to eliminate the internal freedoms and the complete problem solved by only assembling the freedoms on the common boundaries between the substructures. The intermediate solution where the internal freedoms of a substructure have been eliminated giving the super element matrix for the substructure. Also referred to as the Super Element Method.
Substructuring is a form of equation solution method where the structure is split into a series of smaller structures - the substructures. These are solved to eliminate the internal freedoms and the complete problem solved by only assembling the freedoms on the common boundaries between the substructures. The intermediate solution where the internal freedoms of a substructure have been eliminated giving the super element matrix for the substructure. Also referred to as the Substructuring Method.
For a linear system the response is the same if it is found by adding together two or more separate forcing functions and then solving the equations or by solving for the separate forcing functions and then adding the responses together. The second method of solving for each forcing function and adding the response is superposition.
Degrees of freedom where the variable is known before the solution is found. Typically the zero displacements at fixed points in a structural analysis or the points of known temperature in a heat conduction analysis. Generally there must be some points of known value (i.e the structure must be supported) before the equations can be solved.
A matrix is symmetric if it is square and if the ij term is equal to the ji term. See also Skew Symmetric Matrix if it is square and if the ij term is equal to minus the ji term. All of the diagonal terms are zero. A matrix is Hermitian if it is square, the real part is symmetric and the imaginary part is skew symmetric.
In constructing a finite element model, the meshing of similar shapes with similar loading within the model can be avoided by using the principles of symmetry, and by using suitable boundary conditions. The different types of symmetry include: repetitive, mirror, axial and cyclic. Asymmetric loading can also be modelled with suitable boundary conditions.
The matrix of coefficients corresponding to the derivatives of the residual forces with respect to the displacement degrees of freedom: this matrix is evaluated and factorised during the incremental-iterative solution procedure.
An information system designed to manage physical testing from a test request to final results and conclusions. Such systems typically include high sampling rate data acquisition and processing capabilities to manage real time tests.
In a shell element the geometry is very much thinner in one direction than the other two. It can then be assumed stresses can only vary linearly at most in the thickness direction. If the transverse shear strains are not ignored then a thick shell model is formed. This uses the Mindlin shell theory. For the finite element method the thick shell theory generates the most reliable form of shell elements. There are two forms of such elements, the Mindlin shell and the Semi-Loof shell. See also Thin Shell Element.
In a shell element the geometry is very much thinner in one direction than the other two. It can then be assumed stresses can only vary linearly at most in the thickness direction. If the through thickness shear strains can be taken as zero then a thin shell model is formed. This uses the Kirchoff shell theory. See also Thick Shell Element.
Methods for integrating the governing equations of time dependent non-linear problems. Examples include Newmark’s family of methods for solving the transient dynamic equilibrium equations and time marching procedures for creep analysis. See also Newmark Method.
Solution techniques that transform coordinate and force systems to generate a simpler form of solution. The Eigenvectors can be used to transform coupled dynamic equations to a series of single degree of freedom equations.
Special elements that have sides with different numbers of nodes. They are used to couple elements with different orders of interpolation, typically a transition element with two nodes on one edge and three on another is used to couple a 4-node quad to an 8-node quad.
The square root of the ratio of the stiffness to the mass (the square root of the Eigenvalues). It is the frequency at which an undamped system vibrates naturally. A system with n degrees of freedom has n natural frequencies.
The assumed stress form of the finite element solution gives an upper bound on the maximum stresses and strain energy (i.e. these are over estimated) for a given set of displacements. See also Strain Energy.
Equivalent stress measures to represent the maximum shear stress in a material. These are used to characterise flow failures (e.g. plasticity and creep). From test results the Von-Mises form seems more accurate but the Tresca form is easier to handle.
The wavefront of a symmetric matrix is the maximum number of active nodes at any time during a Frontal Solution process. It is a measure of the time required to factorise the equations in a frontal solution. It is minimised be element renumbering.
A technique for transforming a set of partial differential equations to a set of simultaneous equations so that the solution to the simultaneous equations satisfy the partial differential equations in a mean sense.The form used in the finite element method is the Galerkin Method. This leads to identical equations to those from virtual work arguments.
Within a digital computer a number is only held to a finite number of significant figures. A 32bit (single precision) word has about 7 significant figures. A 64bit (double precision) word has about 13 significant figures. All finite element calculations should be conducted in double precision.
A general term for data management systems independent of a specific discipline. Therefore, an Simulation Data Management system is, in this sense, an xDM system configured for the management of simulation data
In the theory of plasticity, a law defining the limit of elastic behaviour under any possible combination of the stress components at any point: the criteria of Tresca and Von Mises Equivalent Stress are common for metals.