We study the dispersion and dissipation of the numerical scheme obtained by taking a weighted averaging of the consistent (finite element) mass matrix and lumped (spectral element) mass matrix for the small wavenumber limit. We find and prove that for the optimum blending the resulting scheme (a) provides 2p + 4 order accuracy for p-th order method (two orders more accurate compared with finite and spectral element schemes); (b) has an absolute accuracy which is O(p −3) and O(p −2) times better than that of the pure finite and spectral element schemes respectively; (c) tends to exhibit phase lag. Moreover, we show that the optimally blended scheme can be efficiently implemented merely by replacing the usual Gaussian quadrature rule used to assemble the mass and stiffness matrices by novel non-standard quadrature rules which are also derived.

If the nodes for the spectral element method are chosen to be the Gauss-Legendre-Lobatto points, then the resulting mass matrix is diagonal and the method is sometimes then described as the Gauss-point mass lumped finite element scheme. We study the dispersive behaviour of the scheme issue in detail and provide both a qualitative description of the nature of the dispersive and dissipative behaviour of the scheme along with precise quantitative statements of the accuracy in terms of the mesh size and the order of the scheme. We prove that (a) the Gausspoint mass lumped scheme (i.e. spectral element method) tends to exhibit phase lag whereas the (consistent) finite element scheme tends to exhibit phase lead; (b) the absolute accuracy of the spectral element scheme is 1/p times better than that of the finite element scheme despite the use of numerical integration; (c) when the order p, the mesh-size h and the frequency of the wave ω satisfy 2p + 1 ≈ ωh the true wave is essentially fully resolved. As a consequence, one obtains a proof of the general rule of thumb sometimes quoted in the context of spectral element methods: π modes per wavelength are needed to resolve a wave.

This paper presents results of detailed nonlinear finite element analysis of gasketed bolted flange pipe joints of different sizes (1, 4, 5, 6, 8, 10, 20 in.) of 900# pressure class for achieving proper preload close to the target stress values with and without considering yielding at bolt and flange and gasket crushing recommended by ASME and industrial guidelines for optimized performance using customized optimization algorithm. In addition, two strategies torque control method and stretch control method are used which is a normal practice in the industry.

Achieving a proper preload in the bolts of a gasketed bolted flanged pipe joint during joint assembly is considered important for its optimized performance. This paper presents results of detailed non-linear finite element analysis of an optimized bolt tightening strategy of different joint sizes for achieving proper preload close to the target stress values. Industrial guidelines are considered for applying recommended target stress values with TCM (torque control method) and SCM (stretch control method) using a customized optimization algorithm. Different joint components performance is observed and discussed in detail