# Finite Element Analysis of Bolted Flange Connections

2014-02-26 14:45:47 COMMENT：0 HITS：

A method of engineering design known as finite-element analysis (FEA) has progressed rapidly in recent years. Traditionally, it is used by structural or mechanical engineers to analyze the stresses or flows of fluids in equipment or systems. Now, however, it is becoming widely available for more focused analyses, such as flange connections in process equipment.

FEA offers considerable advantages for this application. It can be a tool to solve nagging process problems such as leaking flanges, which are now important performance issues with the regulation of fugitive emissions. More importantly, it can be used to predict performance, thereby avoiding problems once a process unit is built and put into operation. Flexitallic Group, a leading supplier of industrial sealing systems, now offers FEA analysis as a service to its clients. This has resulted in several notable cases where processing problems have been reduced or avoided.

What is FEA?

FEA is a computer-aided numerical technique for the prediction of performance of structures under static, dynamic or thermal loads. FEA is a process whereby the response of a physical object exposed to some stimulus is numerically simulated. For example, the compression (response) of a gasket (physical object) as a result of loading (stimulus) by the flanges can be predicted using the FE method (Figure 1).

Figure 1. FEA calculates the stress/strain response to loading

Crucial to the accuracy of this predicted response is the mathematical model or set of equations selected to mimic the object's behavior. These equations are termed the material model. There are numerous types of stress-strain relationships to which mathematical equations can be fitted or for which material models can be defined, the most common being elastic and elastic-plastic. Typically, gasket material exhibits a non-linear visco-elastoplastic relationship as shown in Figure 2.

The FEA Procedure

FEA involves three essential stages; pre-processing, solving and post-processing. During preprocessing, a computer model of the structure is generated and divided up into smaller blocks or elements, appearing as a "discretized" mesh superimposed over the structure. These elements are defined in space by nodes, at which the stress strain computations occur. The greater the number of computation points (nodes), the more closely the solution approaches a unique solution. During solving, the FE solver generates a stiffness matrix for each element, the displacements due to an applied load, and then assembles each element's contribution to form a response matrix for the whole model. Once an equilibrium condition has been achieved, the results can then be imported into a "post-processor" for interpretation.

Figure 2. Stress/strain curve describing the non-linear visco-elastoplastic response of a material

FEA Assumptions

The generation of a 3D model is a complex and time consuming process, often taking days or weeks of work. Depending on the symmetry of a 3D structure, reductions in the model geometry about any planes of symmetry will invariably be made. This can result in ½, ¼ or even 2D models. Circular structures, such as weld neck flange assemblies, for which any radial section can be regarded as being the same as any other, can be reduced to 2D sections know as axisymmetric models (Figure 3). Such axisymmetric models, when compared to their 3D counterparts, have the advantage that mesh densities can be increased, thereby increasing the potential accuracy of the results.

Figure 3. Model definition of a circular flange can be simplified using the principal of axisymmetry

Since an axisymmetric model assumes a state of symmetry in a radial sense, the effect of external bending moments cannot be accounted for. Assumptions about the distribution of the bolts in an axisymmetric representation have to be made. The representation of bolts in this manner has been verified against full 3D models for 4 and more bolts.

Similarly, a series of assumptions must be made to model material properties of bolts, flanges and gasketing materials. For SWG and sheet gaskets, the stress/strain behavior is known to be complex. Material models currently available in commercial software codes are not able to accurately model this visco-elastoplastic behavior. In order that FE analyses involving Flexitallic gaskets can accurately predict their response, a specific customized material model has been developed.

Lastly, the model must be loaded and constrained by a series of loads and boundary conditions, which are representative of the loads and restraints on the real structure. Contact conditions between all discrete entities, such as between the sealing element and inner-ring or flange face, need to be defined if realistic solutions are to be calculated. Contact conditions include friction and thermal conductance properties.

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