Part 1 of the series on Q&A for past analysis and design defense questions

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This post was last edited by B0SS on 2018-4-17 at 21:45. 1. Self-introduction (university graduated from, current company, job responsibilities, etc.)? 2. Present your analysis defense report: model establishment, load and displacement boundary conditions, analysis results, post-processing, conclusions, etc.? 3. What is the difference between conventional design and analytical design for pressure vessels? 【Conventional design method】The thickness of the component is calculated based on film stress, using elastic failure as the criterion. The maximum stress is limited to not exceed a certain allowable value (usually 1 times the allowable stress). The local stresses such as the relatively large edge stresses present in the container are represented in the form of a stress intensification factor, and the maximum stress after accounting for these local stresses is assigned the same allowable strength value as that of membrane stress. The thicknesses of internal pressure cylinders and spherical shells specified in the GB/T150 standard are calculated based on the membrane stress within these components (the primary overall membrane stress), with this stress being kept at 1 time the allowable stress level. For the thickness of elliptical and disc-shaped heads, the local stresses resulting from the effects at the head and cylinder edges are taken into account, and the maximum stress obtained by superimposing these stresses on the membrane stress is controlled to be within 1 time the allowable stress. Conventional design methods are straightforward, but not entirely rational, and tend to be conservative. The [analytical design method] is based on plastic and elastoplastic failure criteria; it takes into account various stresses within the container, such as overall membrane stress, edge stress, and peak stress, to carry out accurate calculations. The stresses are classified, and different strength constraints are applied according to the various forms of failure caused by each type of stress, thereby enabling the calculation of the thickness of the components. Containers designed according to this method are more scientific, rational, safe, and reliable, and can also achieve certain economic benefits. The thickness calculations for various components in the JB/T4732 standard are based on stress analysis and utilize the third strength theory. Among them, although the calculation formulas for internal pressure cylinders and spherical shells are formally identical to the corresponding formulas in GB/T150, their mathematical meanings are completely different. Analytical design, by distinguishing the nature and effects of various stresses, fully utilizes the load-bearing capacity of materials; as a result, it imposes high technical requirements on materials as well as on manufacturing and inspection processes. 4. What is the scope of application for JB/T4732? 1). Containers with a design pressure of 0.1 MPa or greater and less than 100 MPa ； 2). Containers with a vacuum level of 0.02 MPa or higher ； 3). The design temperature should be lower than the corresponding temperature at which creep controls its allowable stress strength. 5. Why is the lower end of the cone shell controlled using 1.1 times the allowable stress? A local stress zone refers to an area in which the distance extending in the meridional direction is no greater than (Disδr/2)0.5, and the stress intensity exceeds 1.1 times the allowable stress; according to the analysis and design standard JB/T4732, a control value of 1.5 times the allowable stress should be used. For the small end of the conical shell, the overall stress level is relatively high. If a control value of 1.5 times the allowable stress is used, the range where the local film stress exceeds 1.1 times the allowable stress will be greater than (Disδr/2)0.5; therefore, to ensure safety, 1.1 times the allowable stress is used as the control value here. 6. The principle of virtual work and St-Venant’s principle? The [Principle of Virtual Work], also known as the Principle of Virtual Displacement, was established by Lagrange in 1764. Its content is: for a system of particles that was originally at rest, if the constraints are ideal bilateral constant constraints, then the condition for the system to remain at rest is that the sum of the works done by all the external forces acting on the system with respect to the virtual displacements of their points of application is zero. The [St. Venant’s principle] is a fundamental principle of elasticity mechanics. It states that the stress in a body caused by a load applied over a small area (or volume) on the elastomer, at a location slightly away from the area where the load is applied, is essentially determined only by the resultant force and resultant moment of the load ； The specific distribution of the load only affects the stress distribution in the area near the load application point. There is another equivalent way of putting it: if the resultant force and the resultant moment of the loads acting on a small area (or volume) of the elastomer are both equal to zero, then the stress at locations far away from the area where the loads act is essentially zero. 7. Reaction spectrum analysis and time-history analysis? The [response spectrum analysis method] is a quasi-static approach that, although it can take into account both the maximum amplitude of vibrations in various frequency bands of a structure and the spectral characteristics, fails to address the factor of duration. Damage investigations have shown that some structures designed using response spectrum theory suffered severe damage even in earthquakes that did not exceed the design intensity, which clearly demonstrates that the factor of duration should be considered in the design process. The response spectrum method ignores the randomness of seismic actions and cannot account for the phenomenon whereby, as a structure gradually enters the plastic state during extreme earthquakes, its internal forces are redistributed due to changes in its dynamic characteristics such as period, damping, and mode shapes. The response spectrum method assumes that the seismic motion at all supports of the structure is identical, ignoring the interaction between the foundation and the soil layer. [Time-history analysis method] is a dynamic analysis technique that directly solves the structural dynamic equations through step-by-step integration. Time-history analysis can provide the entire process of a structure’s seismic response, as well as the internal forces and deformation states of various components at the point when they enter the plastic deformation stage during an earthquake; this enables the identification of the structure’s weak points. This method is a relatively sophisticated one; it can take into account the redistribution of internal forces once the structure enters the plastic state, as well as record the entire process of the structure’s response. However, it only reflects the performance of a structure under the action of a specific seismic wave, and often lacks universality. 8. Boundary conditions for forces and displacements on symmetric and antisymmetric surfaces? On the symmetry plane, the normal displacement is zero, and the stress in the tangential direction is 0 ； On an antisymmetric surface, the tangential displacement is 0 and the normal stress is 0. 9. Does JB/T4732 allow the use of reinforcing rings? 1). The minimum standard tensile strength of steel at room temperature is less than or equal to 540 MPa ； 2). The thickness of the reinforcement ring is less than or equal to 1.5 times the wall thickness ； 3). The nominal thickness of the rotating shell is less than or equal to 38 mm. 10. Adjustment of the safety factor for the new solid content specification: tensile strength becomes 2.4. Which materials are affected? It has a significant impact on high-strength steel, but a minor impact on carbon steel and low-alloy steel. 11. Concept of stress: primary stress, secondary stress, and peak stress, with examples? 【Primary stress】 is the normal or shear stress necessary to balance pressure and other mechanical loads. For an ideal plastic material, the overall plastic flow induced by a single stress is unconfined; that is, when the plastic zone within the structure expands to the point where it becomes a geometrically variable mechanism, a limiting state is reached. Even if the load is no longer increased, uncontrolled plastic flow continues to occur until failure occurs. Primary stress is divided into: primary overall film stress (for example, the film stress resulting from the equilibrium internal pressure or distributed loads in various housings) ； A localized film stress (for example, the film stress caused by external loads and moments at the fixed supports or nozzles of the shell) ； Bending stress: The bending stress that is distributed linearly across the thickness of the cross-section, as required to counteract pressure or other mechanical loads (for example, the bending stress caused by internal pressure at the center of a flat cover) ； (A typical band of evenly arranged tube holes) 【Secondary stress】 refers to the normal or shear stress required to meet external constraint conditions or the requirement for continuous deformation of the structure itself. The basic characteristic of secondary stress is its self-limiting nature; that is, local yielding and a small amount of deformation are sufficient to satisfy the constraints or the requirements for continuous deformation, thereby preventing further increase in deformation. As long as it is not loaded repeatedly, secondary stress will not cause structural failure. (For example: overall thermal stress and bending stress at overall structural discontinuities) ； 【Peak stress】The stress increment added to the primary and secondary stresses, caused by local structural discontinuities or local thermal stresses. Peak stress is characterized by both self-limitation and locality; it does not cause significant deformation ； Its hazard lies in the fact that it may cause fatigue cracks or brittle fracture. (For example: the stress distributed non-linearly along the thickness in the stress increase caused by local structural discontinuities at the shell nozzle connections) ； Thermal stress in the cladding of composite steel plate vessels). 12. Is there discontinuity between the overall structure and the local structure? 【Overall structural discontinuity】 refers to discontinuities in geometry or material that cause changes in stress or strain over a large area of the structure, thereby having a significant impact on the overall stress distribution and deformation of the structure. Examples include the joints where end caps, flanges, connections, supports meet the shell, as well as joints between shells with different diameters or wall thicknesses. 【Local structural discontinuity】 refers to discontinuities in geometry or material that cause only slight changes in stress or strain within a very small area of the structure, with no significant impact on the overall stress distribution and deformation of the structure. Examples include small transition radii, the junctions between the shell and minor attachments, as well as welds that have not been fully penetrated. 13. How are seismic forces considered in the analysis design? Horizontal and vertical seismic accelerations can be applied to consider the effect of seismic forces on the equipment. 14. Perform hexahedral meshing on irregular regions? 1) Use volume mapping for mesh division: The shape of the volume should be block-shaped (6 faces), wedge-shaped (5 faces), or tetrahedral ； The opposite sides of a polyhedron must be divided into the same number of elements, or the division must follow a transition grid pattern, which is applicable to the triangulation of hexahedral grids ； If the body is a prism or a tetrahedron, the number of element divisions on the triangular faces must be even. When the number of faces of the composite body exceeds the aforementioned limit, the number of faces must be reduced to perform mesh generation. Addition or connection operations can be performed on opposite sides; if there is a boundary line between the connected surfaces, that line must be connected as well, with the surfaces being connected first and then the lines. 2) Mesh generation using volume sweeping method: Volume elements can be generated by sweeping a mesh from one interface across the entire volume (which must exist and not yet have a mesh). If the source surface mesh is composed of quadrilateral meshes, a hexahedral mesh is generated. If the surface is composed of a triangular mesh, wedge elements are generated. If the surface is composed of triangles and quadrilaterals, then the solid is filled by wedges and hexahedra. 3) Divide irregular-shaped volumes into relatively regular ones, specify the number of segments for each line of the volume, and use hexahedral elements for mesh generation. 15. Principle of stress equivalent linearization? The linearization method originates from plate and shell theory. In plate-shell theory, both membrane stress and bending stress are normal stresses parallel to the midplane, distributed uniformly along the thickness respectively and linearly. The transverse shear stress varies parabolically across the thickness; it is neither film stress nor bending stress. The so-called equivalent linearization method involves decomposing the stress distribution curve calculated based on the static equivalent principle into three components: one component is equivalent to the resultant force and represents a thin-film stress that is uniformly distributed along the thickness of the cross-section (or along the Stress Classification Line, SCL) ； The second part is equivalent to the resultant moment, and represents the bending stress that is distributed linearly along the thickness of the cross-section (or SCL) ； The third part is the peak stress with zero resultant force and moment, which varies nonlinearly along the section thickness (or SCL).