General Provisions for the Analysis and Design Process of Pressure Vessels

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When encountering a structure or device, how do we design it? This paper discusses aspects such as the scope of stress analysis design, design pressure, temperature, load determination, material property parameters, establishment of mechanical models, stress intensity assessment, fatigue strength assessment, special manufacturing and inspection requirements, and the preparation of stress analysis reports, with the aim of providing a general set of guidelines for the stress analysis design process. 1. What types of structures require stress analysis? When a structure or pressure vessel meets one of the following conditions, it can be analyzed and designed in accordance with JB/T4732-1995 \"Steel Pressure Vessels – Criteria for Analytical Design\" (confirmed in 2005) or Appendix D of GB/T12337-2014 \"Steel Spherical Storage Tanks\": a) For pressure vessels and their pressure-bearing components that are subjected to cyclic loads, and whose operating conditions do not meet the relevant requirements specified in 3.10 of JB/T4732, fatigue analysis and assessment shall be carried out in accordance with Appendix C of JB/T4732 ； b) For pressure vessels or pressure components whose structural dimensions cannot be determined in accordance with GB/T150, design shall be carried out through stress analysis calculations and evaluations, including the finite element method ； C) Pressure vessels that require an analytical design approach after a comprehensive evaluation based on their design requirements, material properties, manufacturing complexity, and cost-effectiveness, such as large high-pressure reactors and high-pressure vessels ； d) For spherical storage tanks with larger diameters or higher pressures, considering factors such as cost-effectiveness, stress analysis should be employed for design purposes in accordance with Appendix D of GB/T12337 ； e) Pressure vessels for which the owner requests stress analysis and design. 2. How to determine the design temperature, pressure, and load? (1) The design pressure, temperature, and load are determined in accordance with sections 3.6.3.1, 3.6.3.2, and 3.6.3.3 of JB/T4732, as well as standards such as GB/T12337, GB/T151, NB/T47041, and NB/T47042. If any load varies over time, a load frequency curve should be developed to represent the variation of each specific load over time. The load frequency curve should include the corresponding number of cycles or time periods for all operating temperatures, pressures, additional loads, as well as all significant processes acting on the component. (2) The design loads include: internal pressure, external pressure, hydrostatic head, the weight of the container itself (including the gravitational load of the contents), additional loads (gravitational loads of auxiliary equipment, pipelines, and external fittings, etc.), cyclic loads, reaction forces caused by supporting accessories, thermal stress loads due to temperature variations, wind loads, seismic loads, snow loads, etc. 3. How to obtain material property parameters? (1) The elastic modulus, Poisson’s ratio, thermal expansion coefficient, thermal conductivity, thermal diffusivity, density, and specific heat capacity of the materials shall be selected in accordance with GB/T150, GB/T151, ASME Section II, Division D, and relevant standards. (2) Method for determining allowable stress: a) For compressive components of local structures designed using the \"analytical design method\", the allowable stress of the materials shall be selected in accordance with GB/T150.2 ； b) The design stress strength of the material for the compression members, whose overall structure is designed using the \"analysis and design method\", shall be selected in accordance with the provisions of JB/T4732 ； c) The design stress intensity for spherical storage tanks designed using the \"analytical design method\" shall be selected in accordance with the provisions of Appendix D in standard GB/T12337 ； d) When materials of foreign grades are used, the allowable stress or design stress intensity shall be calculated in accordance with GB/T150.1 (for partially stressed structures designed by analysis methods) or JB/T4732 (for fully stressed structures designed by analysis methods), and it shall not exceed the allowable stress value for the corresponding materials as specified in the relevant foreign pressure vessel codes. (3) The stress-strain curves can be selected with reference to Appendix 3.D of ASME VIII-2, including elastic-ideal plastic and true stress-strain curves considering strain hardening, cyclic stress-strain curves, and stable true stress-strain amplitude curves. 4. How to establish a mechanical model? The mechanical model of the structure is derived based on fundamental concepts such as elasticity theory, shell theory, plasticity theory, and the finite element method, as well as the structural characteristics and loading conditions. To determine the nature of an analytical problem, the following approach can be followed: a) In equilibrium equations, stress-strain relationships, strain-displacement relationships, boundary conditions, and connection conditions, if there are nonlinear terms between the variables in any of these relationships, then the problem is considered nonlinear ； b) A problem can be considered static only when all variables and relationships are independent of time ； c) When there is a large temperature gradient in the structure (including spatial and temporal temperature gradients), thermal conduction analysis and thermal stress analysis should be conducted. When thermal stress is very small or not the dominant stress compared to others, thermal stress can be ignored ； d) When the material undergoes local plastic deformation, design can still be carried out based on elastic analysis ； When the material undergoes large-scale plastic deformation, it should be treated as a plasticity problem or an elastoplasticity problem. 5. How to simplify the model? Complex structures are simplified into typical elements such as bars, beams, plates, shells, and blocks, based on the geometric characteristics of their various parts as well as the distribution of loads ； When the structure of the 3D model under analysis and the loads are perfectly symmetric, it can be simplified to a 2D planar structure ； When the structure satisfies periodic symmetry conditions, a 1/n model (where n is the number of periods) can be established, etc. The simplification of the model is based on the principle of ensuring the accuracy of the analysis results at the locations of interest as much as possible. 6. How to select a unit? For finite element numerical simulations using ANSYS Mechanical APDL, element types with intermediate nodes should be preferred. For stress analysis, fatigue analysis, etc., the 3D solid Solid186 high-order elements are preferred (with the corresponding temperature elements being Solid90); when the number of computational elements is large, the Solid185 low-order elements can also be used (with the corresponding temperature elements being Solid70) ； For buckling analysis, ultimate load analysis, modal analysis, etc., the Shell181 shell element is preferred ； For two-dimensional planar structures, the Plane82 element is preferred ； For beam structures, the Beam189 beam element is preferred ； When performing contact analysis, the Conta173 contact element and the Targe170 target element should be preferred ； Inter195 gasket units should be preferred as gaskets ； For quality elements, Mass21 is preferred ； The selection of the remaining units can be found in the ANSYS 14.5 help file. Depending on the structural characteristics, different units can also be selected for combination. For other finite element simulation software, the element types should be selected in accordance with the aforementioned principles. 7. How to perform grid partitioning? (1) For 3D solid structures, hexahedral meshes should be used preferentially ； Quadrilateral grids are preferred for shell structures or two-dimensional planar structures. The side length ratio of the ideal element is 1; for acceptable elements, the range of side length ratios is less than 3 for linear elements and less than 10 for quadratic elements. (2) When meshing the model, ensure that adjacent elements of the multi-body model share nodes at their boundaries ； When the degrees of freedom of the element types used in adjacent bodies differ, their degrees of freedom can be coordinated using methods such as constraint equation method, multiple-point constraint (MPC) method, stiffness superposition method, composite element method, and orthogonal shell coupling method. For assemblies, it is usually necessary to define contact pairs. (3) While considering the economic efficiency of the grid, the reliability of the grid computing results should be ensured. The usual approach is to double the original grid density; if the results of the two calculations differ by less than 3%, it proves that the original grid density is reliable ； Otherwise, the grid density should be modified again and the above process repeated until the grid density meets the reliability requirements. 8. How to apply loads and boundary conditions? The various combinations of design loads and test loads are determined in accordance with Table 3-3 of standard JB/T4732; the load combination conditions for stress analysis of spherical tanks are determined in accordance with Section D.4.3 of Appendix D of standard GB/T12337. The load condition combinations that need to be analyzed also depend on the actual situation; if multiple conditions arise during operation, each one should be analyzed separately. The application of boundary conditions should comply with the actual constraints of the structure: a) Load conditions: Define the location, direction, and magnitude of node loads, element edge loads, surface forces, body forces, and temperature loads in the model ； b) Thermal boundary conditions: Define the location, magnitude, or behavior of node temperatures, heat conduction, convective heat transfer, and radiative heat transfer in the model ； c) Displacement constraint conditions: Specify the constraints on the displacements of nodes and node degrees of freedom in the model, as well as the type and magnitude of these constraints ； d) Other boundary conditions: Define other boundary conditions used for analysis, such as primary and secondary degrees of freedom, connection degrees of freedom, or motion degrees of freedom in the model. 9. How to perform stress intensity assessment? a) After the finite element stress analysis is completed, the custom path should be perpendicular to the isostress lines of the highest stress component; the custom path should also be perpendicular to the midplane of the cross-section in order to achieve similar accuracy. By linearizing the stress along this path, it is possible to determine the film stress, bending stress, film+bending stress, peak stress, and total stress. b) Stress classification is based on Table 4-1 and Table 5-3 in JB/T4732. The designer determines the nature of film stress (primary global film or primary local film) and bending stress (primary bending stress or secondary stress) by considering factors such as the extent to which stress contributes to the failure of the container’s strength, the area and distribution pattern of the stress, the causes of the stress, and its impact on failure. c) The value of the stress strength limit is determined in accordance with Sections 5.2 and 5.3 and Table 5-1 of JB/T4732, while the load combination factor is based on Table 3-3 of JB/T4732. d) For the local film stress at the small end of the conical shell, 1.1 times the design stress intensity shall be used as the control value ； For large openings, at the location where the angle between the nozzle root and the longitudinal axis of the shell is 90 degrees, the bending stress shall be considered as a primary stress. 10. How to evaluate fatigue strength? a) The calculation of the alternating stress intensity factor Salt is divided into two cases: when the direction of the principal stresses at the considered point remains constant during the cycle, and when it changes. It is calculated in accordance with Section C.2.1 of Appendix C to JB/T4732; only the stresses induced by the specified operating cycle need to be taken into account, without considering any stresses resulting from loads or temperature conditions that remain unchanged throughout the cycle. b) Application of designing fatigue curves, in accordance with C.2.2 in Appendix C of JB/T4732. c) Cumulative damage: When there are two or more significant stress cycles, the effect of fatigue cumulative damage shall be calculated using the method specified in Section C.2.4 of Appendix C to JB/T4732. d) The bolt fatigue strength is in accordance with C.5 of Appendix C in JB/T4732. e) The fatigue strength verification shall be carried out in accordance with C.2.2 c) of Appendix C in JB/T4732; if replaceable components such as studs have a different service life from that of the container, the service life of the studs shall be specified separately in the design drawings. 11. What special manufacturing and inspection requirements are needed for stress analysis of design structures and containers? In addition to complying with JB/T4732, GB/T12337 and related standards regarding the manufacturing and inspection of containers, the design documents shall also specify the following requirements, although these are not exhaustive: a) For pressure vessels designed for fatigue analysis (under cyclic loading), the inner and outer surfaces of the welds in welding joints of types A and B shall be level with the surface of the base metal; no excess height is allowed. b) For pressure vessels designed based on fatigue analysis (under cyclic loading), it is not allowed to use welder’s stamps; the manufacturing unit shall establish a separate method for verifying welder markings. c) Weld joints of categories A and B shall be subject to 100% radiographic or ultrasonic testing in accordance with the methods specified in the drawings, and the feasibility of such testing shall be considered in the structural design. d) Studs with a diameter larger than M36 must undergo magnetic particle or penetrant testing. 12. How to write a stress analysis report? A complete stress analysis report should include the following: a) Load analysis: design parameters, equipment schematic, material property data ； b) Calculation of the strength of main components ； c) Structural analysis and mechanical model: structural geometric parameters, finite element model, loads and boundary conditions ； d) Stress analysis results ； e) Stress strength assessment ； f) Fatigue strength assessment (for fatigue-resistant pressure vessels): Pressure vessels (except studs), studs ； g) Conclusion ； h) Main technical specifications ； i) Appendix: Data on stress linearization along the path, calculations for supports, or calculations for components designed using the \"rule-based design method\", etc. ​ The above are some of the author’s personal opinions; there may be inaccuracies, so everyone is welcome to discuss them!