An implicit solution method for integrating second order equations of motion. It can be made unconditionally stable. Also referred to as the Newmark Method.

An implicit solution method for integrating second order equations of motion. It can be made unconditionally stable. Also referred to as the Newmark Beta Method

An incremental-iterative non-linear procedure to solve the equilibrium equations: the tangential stiffness matrix is updated during every iteration of every increment. See also Newton-Raphson Non-Linear Solution

A general technique for solving non-linear equations. If the function and its derivative are known at any point then the Newton-Raphson method is second order convergent. See also Tangent Stiffness Matrix.

The element behaviour is defined by the response at the nodes of the elements. Nodes are always at the corners of the element, higher order elements have nodes at mid-edge or other edge positions and some elements have nodes on faces or within the element volume. The behaviour of the element is defined by the variables at the node. For a stiffness matrix the variables are the structural displacement, for a heat conduction analysis the nodal variable is the temperature. Other problems have other nodal variables.

Elements that do not satisfy compatibility either within the element or across element boundaries or both. Such elements are not generally reliable although they might give very good solutions in some circumstances.

When at least one of the coefficients of stiffness, mass or damping vary with displacement or time then the system is non-linear.Superposition cannot be used to solve the problem.

A particular plastic flow rule to ensure that the plastic strain components are in a ratio such that their resultant is in a direction normal to the yield surface. See also Flow Rule.

The process of integrating the element stiffness matrix based on numerical algorithms such as Gaussian quadrature. Evaluations are made at strategic points within each element, known as Gauss Points.

The minimum number of Gauss points required to integrate an element matrix. Also the Gauss points at which the stresses are most accurate, see also Reduced Integration.

A material where the response to load depends on the direction within the material. It is less general than anisotropy, and up to 12 independent constants are required to relate stress and strain.

A system that has an equation of motion where the damping is greater than critical. It has an exponentially decaying, non-oscillatory impulse response. See also Critical Damping.

Initial studies conducted on small simplified models to determine the important parameters in the solution of a problem. These are often used to determine the basic mesh density required. Also referred to as Pilot Studies.

The fraction of the mass that is active for a given mode with a given distribution of dynamic loads. Often this is only defined for a specific load case of inertia (seismic) loads.

A simple element type test using a patch of several elements, one of which is arbitrarily orientated with respect to the global co-ordinates. If the patch is loaded by displacements consistent with a state of constant strain and the strain inside the selected element is constant, the test is passed. See also Continuum Region Element (CRE) Method.

In the context of contact algorithms, a constraint on stiffness behaviour usually applied via large numbers in the equations, e.g. by introducing stiff springs. Also referred to as Penalty Stiffness.

In the context of contact algorithms, a constraint on stiffness behaviour usually applied via large numbers in the equations, e.g. by introducing stiff springs. Also referred to as Penalty Function.

The ratio of the in-phase component of a signal to its out-of-phase component gives the tangent of the phase angle of the signal relative to some reference.

When a substance subjected to temperature changes transforms from solid to liquid or gaseous state. During this phase change, latent heat is either released or absorbed.

Initial studies conducted on small simplified models to determine the important parameters in the solution of a problem. These are often used to determine the basic mesh density required. Also referred to as Parametric Studies.

A two dimensional analysis is plane stress if the stress in the third direction is assumed zero. This is valid if the dimension of the body in this direction is very small, e.g. a thin plate. See also Plane Stress.

A two dimensional analysis is plane strain if the strain in the third direction is assumed zero. This is valid if the dimension of the body in this direction is very large, e.g. a cross-sectional slice of a long body. See also Plane Strain.

Checks that can be made on the results after the analysis. For a stress analysis these could include how well stress free boundary conditions have been satisfied or how continuous stresses are across elements.

A given crack inside a loaded structure behaves in conditions of PYFM when the crack fields local to the crack tip exhibit considerable plastic behaviour. See also Elastic Plastic Fracture Mechanics (EPFM).

For a hypothetically small increase in crack length or area, this is the amount of potential energy released divided by that length or area. It equals the negative of the Strain Energy Release Rate when elastic conditions predominate. It provides the basis for fracture parameters in post yield fracture mechanics and other non-linear conditions.

The equations relating an increment of stress to an increment of plastic strain for a metal undergoing plastic flow. See also Von Mises Yield Criterion.

A Process Step Items acts as the process step record and tracks the execution of software methods that operate on data items in the SDM repository and their attached files.

An individual who has achieved NAFEMS Professional Simulation Engineer indicating that they have achieved a certain level of competence in the application of simulation and analysis tools in an industrial setting.

The profile of a symmetric matrix is the sum of the number of terms in the lower (or upper) triangle of the matrix ignoring the leading zeros in each row. Embedded zeros are included in the count. It gives a measure of the work required to factorise the matrix when using the Cholesky solution. It is minimised by node renumbering. See also Cholesky Factorisation (Skyline).

A damping matrix that is a linear combination of the mass and stiffness matrices. The eigenvectors of a proportionally damped system are identical to those of the undamped system.

Occurs when all the external loads are applied simultaneously, and increase in proportion to one another throughout the loading history. This clearly does not occur when one component of load is applied and then another.

A technique for finding Eigenvalues This is currently the most stable method for finding eigenvalues but it is restricted in the size of problem that it can solve.

A mode of heat transfer due to electromagnetic waves. Thus, the heat energy can be transferred in a vacuum. It is characterised by the Stefan-Boltzmann law.

Damping that arises from energy being carried away from a vibrating body by expanding pressure waves. Sound radiation is an example of this. Such radiating energy, both to the surrounding fluid and through the supports, often forms the main damping in a vibrating structure.

An analysis undertaken when the applied loading is only known in terms of its statistical properties. The loading is non-deterministic in that its value is not known exactly at any time but its mean, mean square, variance and other statistical quantities are known.

Occurs in Cyclic Loading when plastic strains keep on accumulating incrementally with each cycle, leading to eventual failure via incremental collapse.

The ratio of stiffness times displacement squared (2 x strain energy) to mass times displacement squared. The minimum values of the Rayleigh quotient are the eigenvalues.

The ratio of the steady state displacement response to the value of the forcing function for a sinusoidal excitation. It is the same as the Dynamic Flexibility.

The process of intentionally under-integrating the element stiffness matrix to prevent problems such as Shear Locking or to improve the element’s performance.

A structure where all of the unknowns can not be found from equilibrium considerations alone. The compatibility equations must also be used. In this case the structure is said to be redundant.

The process of documenting, analyzing, tracing, prioritizing and agreeing on requirements and then controlling change and communicating to relevant stakeholders.

The forces which are equal to the applied load minus the internal resisting forces which occur during non-linear solutions: used to measure the state of equilibrium by comparison to the convergence tolerance.

If a displaced shape does not give rise to any strain energy in the structure then this a rigid body mode. A general three dimensional unsupported structure has 6 rigid body modes, 3 translation and 3 rotation.

This is a connection between two non-coincident nodes assuming that the connection is infinitely stiff. This allows the degrees of freedom at one of the nodes (the slave node) to be deleted from the system. It is a form of Multi-Point Constraints.

This is a connection between two non-coincident nodes assuming that the connection is infinitely stiff. This allows the degrees of freedom at one of the nodes (the slave node) to be deleted from the system. It is a form of Multi-Point Constraints.

Computers have a fixed wordlength and hence only hold numbers to a certain number of significant figures. If two close numbers are subtracted one from another then the result loses the first set of significant figures and hence loses accuracy. This is round off error.