Finite Element Modeling of Seismic Response of Field Fabricated Liquefied Natural Gas (LNG) Spherical Storage Vessels

All real physical structures behave dynamically when subjected to loads or displacements. This research paper, therefore, presents seismic response of field fabricated liquefied natural gas spherical storage vessels using finite element analysis. The seismic analysis procedure used represents a practical approach in quantifying the response of spherical storage vessel with its content when it is subjected to seismic loading. In the finite element method approach, six degrees of freedom per node is used for legs/column of the spherical storage tanks. Lumped mass procedure is employed to determine system mass matrix of the structure. Computer programme code is developed for the resulting matrix equation form finite element analysis of the structure using FORTRAN 90 programming language. The modeling of the seismic load utilizes the ground acceleration curve of a site. From the results of the modal analysis, the system is uncoupled thereby gives way to the application of Newmark’s method. Newmark’s method as one of the widely used time-step approach for the seismic response is applied. The developed programme coding is validated with analytical results (P > 0.5). It shows that the approach in this research work can be successfully used in determine the stability of large spherical storage vessels against seismic loadings when base acceleration spectral of the site are known. This approach gives better results than the static-force approach which gives conservative results. While the approach used in this research treats seismic loads as time event, static-force approach assumed that the full ground force due to seismic motion is applied instantaneously.

Finite Element Modelling of Insulation Thicknesses for Cryogenic Products in Spherical Storage Pressure Vessels

This study investigates various insulation thicknesses requirements for double-walled spherical pressure vessels for the storage of cryogenic liquids. The inner tank is suspended from the outer tank by straps or cables and the annular space between the tanks is filled with insulation. The outer tank is not subjected to the freezing temperatures and is thus assumed to be a standard carbon steel sphere. In the Finite Element Analysis model of the system, one dimensional analysis was employed. This is due to the assumption that temperature gradient does only exist along the spherical radial direction. In the developed model, once the thickness of the inner shell has been determined based on relevant standards and codes—ASME Sec VIII Div 1 or 2, BS 5500 etc and the thickness of the outer shell is known;the required insulation material thicknesses were calculated for different insulating materials. Set of equations resulting from Finite Element Analysis were solved with computer programme code which was written in FORTRAN 90 programming language. The results obtained are validated by analytical method. The results showed no significant difference (P > 0.05) with values obtained through analytical method. The thicknesses for different insulating materials in-between inner and outer tank shells were compared. The results showed that as the insulating material thickness was increased, the heat flux into the stored product was decreasing and at a certain thickness;it started increasing. The insulating thickness at which this happens is termed as critical thickness of insulating material—the thickness of insulation at which the heat influx to the stored products is minimal;this would therefore reduce boil-off of the stored cryogenic product. High thermal conductivity insulating materials need to be thicker than lower thermal conductivity insulating materials if the system is conditioned to have the same heat flux into the stored product for all insulating materials. In the simulation, different insulating material gives different minimal heat influx into the stored products.

Finite Element Modeling of Variable Membrane Thickness for Field Fabricated Spherical (LNG) Pressure Vessels

This study investigated thickness requirements for field fabricated (large) spherical liquefied natural gas (LNG) pressure vessels using the finite element method. In the FEM modeling, 3-dimenisonal analysis was used to determine thickness requirements at different sections of a 5-m radius spherical vessels based on the allowable stress of the material as given in ASME Section II Part D. Shallow triangular element based on shallow shell formation was employed using area coordinate system which had been proved better than the global coordinate system in an earlier work of the authors applied to shop built vessels. This element has five degrees of freedom at each corner node-five of which are the essential external degrees of freedom excluding nodal degree of freedom associated with in plane shell rotation. Set of equations resulting from Finite Element Analysis were solved with computer programme code written in FORTRAN 90 while the thickness requirements of each section of spherical pressure vessels subjected to different loading conditions were determined. The results showed membrane thickness decreasing from the base upwards for LNG vessels but constant thickness for compressed gas vessels. The obtained results were validated using values obtained from ASME Section VIII Part UG. The results showed no significant difference (P > 0.05) with values obtained through ASME Section VIII Part UG.

Finite Element Modeling of Stability of Beam-Column Supports for Field Fabricated Spherical Storage Pressure Vessels

Spherical pressure vessels in large sizes are generally supported on legs or columns evenly spaced around the circumference. The legs are attached at or near the equator of the sphere. This research work focussed on flexural-torsional buckling of beam-column supports of field fabricated spherical pressure vessels using finite element analysis. Flexuraltorsional buckling is an important limit state that must be considered in structural steel design and it occurs when a structural member experiences significant out-of-plane bending and twisting. This research has therefore considered the total potential energy equation for the flexural-torsional buckling of a beam-column element. The energy equation was formulated by summing the strain energy and the potential energy of the external loads. The finite element method was applied in conjunction with the energy method to analyze the flexural-torsional buckling of beam-column supports. To apply the finite element method, the displacement functions are assumed to be cubic polynomials, and the shape functions used to derive the element stiffness and element geometric stiffness matrices. The element stiffness and geometric stiffness matrices were assembled to obtain the global stiffness matrices of the structure. The final finite element equation obtained was in the form of an eigenvalue problem. The flexural-torsional buckling loads of the structure were determined by solving for the eigenvalue of the equation. The resulting eigenvalue equation from the finite element analysis was coded using FORTRAN 90 programming language to aid in the analysis process. To validate FORTRAN 90 coding developed for the finite element analysis and the methodology, the results given by the software were compared to existing solutions and showed no significant difference P > 0.05.

Finite Element Modeling of Shop Built Spherical Pressure Vessels

This work builds on an earlier work done which used global coordinates where a large number of elements were needed to form a convergence of results for shop built spherical pressure vessels. In this work area coordinates were used. Any action that leads to an inability on the part of a structure to function as intended is known as failure. This research, therefore, investigates stresses developed in a shop built carbon steel spherical storage vessels using finite element approach as the analytical tool. 3-D finite element modeling using 3-node shallow triangular element with five degrees of freedom at each node is employed. These five degrees of freedom are the essential nodal degrees of freedom without the sixth in-plane rotation. The resulting equations from finite element analysis are coded using FORTRAN 90 computer programme. Spherical storage vessels are subjected to various internal loading pressures while nodal displacements, strains and the corresponding maximum Von-mises stresses are determined. The calculated maximum Vonmises stresses are compared with the yield strength of the shell plate material. Using specified safety factor, safety internal pressures with the corresponding shell thicknesses for shop built spherical pressure vessels are determined. The finite element modeling carried out in this research can be used to predict in-service stresses, strains, and deformations of shop built spherical pressure vessels using Von-mises yield stress as the failure criteria. The results obtained were validated by analytical method and it showed there was no significant difference (P > 0.05) with values obtained through analytical method.