Summary:

A limit load analysis of a pressure vessel with pressure and external force loading was conducted. The limit load was defined by increasing the pressure and the nozzle external loads proportionally until collapse occurred. The evaluation of the limit load analysis was conducted in accordance with ASME BPVC Section VIII Division 2.

The limit load analysis provides insight into the collapse load and failure mode. The results of the limit load analysis and a plastic analysis are compared to the results obtained by linear and nonlinear shell and plate element analyses of the same nozzle. The authors discuss the comparison of the results as there is some variance between the different methodologies.

Scope:

The evaluation of the limit load analysis was conducted in accordance with ASME BPVC Section VIII Division 2

Methodology:

A three-dimensional model of the spherical pressure vessel is built in ANSYS. The model was meshed with higher order elements. Mesh has been refined at the critical locations of the pressure vessel such as nozzle and shell interface.. Fixed restraints  are applied to leg supports. The fixed restraint prevents translation and rotation of the vessel in the X, Y & Z directions.

To perform the limit analysis, a minimum load step of about 0.5 MPa and a starting load step of about 6 MPa were specified. During the analysis, the FE software loaded the structure and kept bisecting the load step until non-convergence occurred with the minimum load step. The last converged solution is, therefore, expected to give the limit load to an accuracy of about 0.5 psi, assuming that the accuracy of the equilibrium iterations is consistent with that of load stepping. To find the limit load, two approaches are used ;

Twice Elastic Slope Method :

The limit load are plotted as the ordinate & the lateral strain as the abscissa. The regression line as determined from the data in the linear elastic range is drawn. The angle that the regression line makes with the ordinate is called ‘Ѳ’.A second straight line ,here after called the collapse limit line ,is drawn through the intersection of regression line with the abscissa so that it makes an angle ф=tan-1 (2tan Ѳ) with the ordinate. The intersection of the collapse limit line with the curve is the limit load as shown in figure.

Tangent Intersection Method:

To calculate limit load of structure there are two test procedures distortion measurement and strain measurement. For distortion measurement tests, the loads are plotted on the ordinate and the lateral strain are plotted on the abscissa. The one tangent is drawn to the elastic zone & similarly another tangent is to plastic zone. The load corresponding to the intersection of the two straight line is defined as the limit load as shown in figure.

Outcome:

From FEA results it is observed that the limit load from tangent intersection method and twice elastic slope method are 4.25 MPa. And 4.1 MPa.