Stresses in Nozzle Shell Junctions due to External Loads: A Comparative Study

Based on a systematic literature review, no design guidelines addressing practical issues related to steel circular hollow section (CHS) members under hydrostatic pressure have been documented thus far, except for the design recommendations proposed by the European standard EN 1993-1-6 concerning the strength and stability of shell structures. Considering that the existing codes are often outdated and subject to improvement, there is a growing demand for modern solutions that can accurately replicate the stability loss response of equipment subject to external pressure. The development of a more direct and simple method, augmented by reliable computational techniques, is advisable to avoid the numerous challenges associated with manual calculations. This approach will streamline the design process and mitigate the complexity of current practical or technical approaches. Thus, this research has formulated a method to predict design strength through the direct application of the critical elastic buckling stress, determined from Generalised Beam Theory (GBT) analyses, induced by hydrostatic pressure in custom-crafted equations, finely tuned for this specific objective. The authors present a formulation of GBT to analyze the elastic buckling behavior of CHS subject to both combined axial compression and external pressure. This work provides an extensive study of the behavior of circular cylindrical shells under external loading conditions. It first introduces the analyses of GBT and the theoretical and empirical formulas applicable to this objective. It then describes the steps involved in the development and validation of a numerical model that simulates the response of circular cylindrical shells under hydrostatic pressure, conducting an extensive parametric study using finite element analyses (FEAs). The results from available tests validate the finite element (FE) model. Upon achieving adequate agreement between the generated numerical and experimental results, new resistance reduction curves for cylindrical shell members are developed based on the results of the parametric study. Additionally, the study compares the existing provisions of EN 1993-1-6 for the design of cylindrical shells under hydrostatic pressure. Finally, a statistical approach is adopted to compare the responses of cylindrical shells calculated according to the EN 1993-1-6 code recommendations with those obtained through the newly proposed method.

Objective To explore the establishment of 3D thoracic model by finite element methods, and study the mechanical mechanism of minimally invasive surgery for correcting the chest wall deformity, and provide personalized surgery solution in the future. Methods According to admission and exclusion criteria, we selected 10 cases of pectus carinatum that received chest CT scan. The finite element model of pectus carinatum was established and analyzed by Mimics, ABAQUS, etc. The validity of finite element method for chest wall was verified by comparing the sternal displacement between the simulated values and actual values with the same force. Results The 3D finite element model of pectus carinatum was successfully established and analyzed. The stress distribution of the 10 cases in the posterior ribs was mainly in the 1-6 ribs on both sides, mostly concentrated in the 4th to 6th ribs, and the stress was symmetrical on both sides. Statistical analysis showed that the displacement value of the sternum was correlated, and the validity of the model was verified. Conclusion Mimics, ABAQUS and other finite element modeling and analysis software can effectively establish the thoracic 3D finite element model and mechanical analysis, which can help the further development of personalized minimally invasive surgery for correcting chest wall deformities. Key words: Pectus carinatum; Chest wall deformity; Finite element analysis

Cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression display the most extreme buckling sensitivity to imperfections. In engineering practice, the reduction of load carrying capacity due to imperfections is usually addressed by use of a knockdown factor to lower the critical buckling stress estimated or computed without accounting for imperfections. For thin elastic cylindrical shells under uniaxial compression and spherical shells under equi-biaxial compression, the knockdown factor is typically as small as 0.2. This paper explores the alleviation of imperfection-sensitivity for loadings with a reduced circumferential (transverse) membrane stress component. The analysis of Koiter (1963) on the effect of an axisymmetric imperfection on the elastic buckling of a cylindrical shell under uniaxial compression is extended to both cylinders and spheres for loadings that produce general combinations of biaxial membrane stresses. Increases in the knockdown factor due to a reduction of the transverse membrane component are remarkably similar for cylindrical and spherical shells.

Buckling of cracked cylindrical thin shells under combined internal pressure and axial compression

PurposeIntegrity assessment is used to ensure reliability operation of a pressurized equipment containing defects. Based on data of cylindrical shell dimensions, operation conditions, material properties and crack dimensions, an assessment can be carried out, using either Level 1, Level 2 or Level 3 procedure. Assessment using Level 3 procedure within the code requires a finite element simulation in order to generate both the evaluation point and the failure assessment diagram (FAD) that serves as the acceptance criteria. The purpose of this paper is to provide the numerical data which are used for integrity assessment of a pressure vessel containing crack. Here, a parametric study has been carried out to generate such result for the cases of longitudinal crack defect in a cylindrical shell for a number of common cases, in terms of thickness-to-radius ratio, crack size ratio and crack aspect ratio.Design/methodology/approachThe evaluation of stress intensity factor is determined through J-integral parameter found using a finite element analysis with a specially meshed strategy incorporating the crack. A comparison is made against stress intensity factor provided by the code.FindingsA good agreement is obtained with percent error of 2.13 percent for low aspect ratio crack, and 0.57 percent for high aspect ratio crack. Furthermore, a study has been carried out using the methodology for 160 cases, covering both cases already available in the code and other cases of crack in cylindrical shells. The result can be used as a complement to the existing tabular data available in the code for Level 2 assessment, to be used for integrity analysis of damaged cylindrical shells based on the FAD criteria.Originality/valueThe result can be used as a complement to the existing tabular data available in the API 579 code for Level 2 assessment, to be used for integrity analysis of damaged cylindrical shells based on the FAD criteria. New equations were generated based on finite element analysis and can be used for Level 3 assessment of the code.

Connecting rod is a major link inside of a internal combustion engine. It is the intermediate member between the piston and the crankshaft. Its primary function is to transmit the push and pull from the piston pin to the crank pin thus converting the reciprocating motion of piston in to rotary motion of the crank. In this paper a static analysis is conducted on a connecting rod of a single cylinder 4-stroke petrol engine. The model is developed using Solid modeling software i.e. PRO/E (creo-parametric). Further finite element analysis is done to determine the von-misses stresses shear stress and strains for the given loading conditions. Keywords - ANSYS Workbench, connecting rod, Finite Element analysis, PRO/E (creo-parametric). I. Introduction Connecting rod is among large volume production component in the internal combustion engine. It connects the piston to the crankshaft and is responsible for transferring power from the piston to the crankshaft and sending it in to transmission. They are different types of materials and production methods used in the creation of connecting rods. The major stresses induced in the connecting rod are a combination of axial and bending stresses in operation. The axial stresses are produced due to cylinder gas pressure (compressive only) and the inertia force arising in account of reciprocating action (both tensile as well as compressive), where as bending stresses are caused due to the centrifugal effects. It consists of a long shank, a small end and a big end. The cross-section of the shank may be rectangular, circular, tubular, I-section or H-section. Generally circular section is used for low speed engines while I-section is preferred for high speed engines. The most common type of manufacturing processes is casting, forging, and powdered metallurgy. Connecting rod is subjected to a complex state of loading. It undergoes high cyclic loads of the order of 10^8 to 10^9 cycles, which range from high compressive loads due to combustion, to high tensile loads due to inertia. Therefore, durability of this component is critical importance. Due to these factors, the connecting rod has been the topic of research for different aspects such as production technology, materials, performance, simulation, fatigue etc. Vivek.c.pathade et al(1) performed stress analysis of I.C Engine connecting rod by finite element method. They modeled connecting rod using pro/E Wildfire 4.0 and ANSYS Workbench 11.0 software. They reported from the theoretical and finite element analysis then the stresses induced in the small end of the connecting rod are greater than the stress induced at the big end. K.surdershn Kumar et al (2), reported on modeling and analysis of two wheeler connecting rod. In this connecting rod is replaced by aluminum reinforced with boron carbide for Suzuki GS150R motor bike. A parametric model of connecting rod is modeled using pro/E Wildfire 4.0. Analysis is carried out by using ANSYS software. They presented the results of materials and reported that the working factor of safety is nearer to theoretical factor of safety in aluminum boron carbide. Anil Kumar et al (3), presented the optimization of connecting rod parameters using CAE tools. They reported on optimizing weight and reducing inertia forces on the existing connecting rod, which is obtained by changing design variables in the existing connecting rod design. The model was developed in pro/E Wildfire 5.0 and then imported as a Para solid (xt) from in ANSYS Workbench. The stress was found maximum at the piston end. This can be reduced by increasing the material near the piston end. The weight of the connecting rod was also reduced by 0.004kg which was not significant but reduces the inertia forces. Suraj pal et al (4), reported on design evaluation and optimization of connecting rod parameters using Finite element method. Proper finite element model is developed using pro/E Wildfire 4.0. The weight of the connecting rod is also reduced by 0.477g. The stress is found maximum at the piston end so that material is increased in the stressed portion to reduce stress. Dr. S B Jaju et al (5), performed modeling and analysis of connecting rod of four stoke single cylinder engine for optimization of cost and material. Their study has dealt with two subjects first static load stress analysis of the connecting rod, and then second optimization for weight.

The inverse problem of elastoplastic deformation of a thick-walled cylindrical shell of finite length under internal pressure is solved. For a given displacement of the outer surface of the shell, it was necessary to construct a numerical technique to determine the internal pressure providing this displacement. The problem being solved is a boundary value problem of a mixed type. The cylindrical shell under study is in a plane stress state and a volumetric deformed state. The mathematical formulation of the problem was based on the provisions of the deformation theory of plasticity. The strain state of the shell was described using nonlinear Hencky strains. The constructed model of elastic-plastic deformation of the shell took into account the compressibility of the material and the nonlinear law of hardening. The numerical calculation method is based on the method of variable elasticity parameters using the method of successive approximations, taking into account changes in the geometry of the shell during deformation. To assess the adequacy of the constructed numerical method for solving the inverse problem, a comparative calculation of the direct problem of elastoplastic deformation using the finite element method in the ANSYS 19.0 software package was carried out. The results obtained for radial and circumferential stresses, stress intensity, radial displacements of the boundary surfaces of a cylindrical shell at internal pressure calculated when solving the inverse elastoplastic problem showed sufficient consistency. The stress distribution patterns in the cylindrical shell wall according to the method of variable elasticity parameters and the finite element method are qualitatively the same. The differences in the quantitative results obtained according to the two approaches are no more than 10%. The proposed calculation method can be used in the field of aircraft engineering in order to calculate the required pressure when deforming cylindrical shells to the required geometry, taking into account the physical and geometric nonlinearities of the material under the condition of monotonic loading.

In this paper, a new solution method is proposed for determining the natural frequency of a given mode for a finite-length circular cylindrical thin shell with a circumferential part-through crack. The governing equation of the cracked cylindrical shell is derived by integrating the line-spring model with the classical thin shell theory. The proposed method calculates the natural frequency from an initial trial to satisfy both the governing equations and appropriate boundary conditions through an optimization process. The initial trial is proposed to satisfy the governing equations by using the beam modal function to determine the modal wavenumbers and mode shapes of cylindrical shells in the axial direction, assuming the flexural mode shapes of cylindrical shells in the axial direction to be of the same form as that of a flexural vibration beam with the same boundary conditions. Four representative sets of boundary conditions are considered: simply supported (SS-SS), clamped-clamped (C-C), clamped-simply supported (C-SS), and clamped-free (C-F). Compared with the finite element (FE) method, the proposed solution method is verified to provide an accurate and efficient way to calculate the dynamic characteristics of both intact and cracked cylindrical shells.

In this paper, a study is carried out to investigate the stress concentrations at junctions of cylindrical-conical shell structures using the finite element method. A finite element solution is developed and used to model the structure. The solution utilizes curved finite elements that are capable to model the cylindrical and conical shell surfaces with high degree of accuracy. Elevated storage cylindrical-conical tanks and silos supported by "unyielding" stiff ring girders, which sit on a cylindrical skirt or on multi equally spaced columns, are analyzed. The opportunity is also taken to investigate the effects of various geometrical parameters, such as the conical angle, the height/radius ratio of the cylindrical shell, the location of the ring girder relative to the junction and the influence of adding ring stiffeners on the behavior of the structure. It is concluded that the geometrical discontinuity at the junction causes concentrations of compressive inplane as well as bending stresses. These stresses can be significantly reduced by either increasing the inclination angle of the conical bottom or by placing the ring girder closer to the junction.

The composite cylindrical shell pressure structure is widely used for autonomous underwater vehicle (AUV). To analyze the critical buckling problem of variable stiffness (VS) composite pressure structure of AUV, a discrete finite element (DFE) method based on the curve fiber path function is developed in this work. A design and optimization method based on the radial basis function surrogate method is proposed to optimize the critical buckling pressure for a VS composite cylindrical shell. Both the DFE and surrogate methods are verified to be valid by comparison with the experimental data from the listed references. The effects of the geometric parameter and fiber angle on the critical buckling pressure are studied for different cylindrical shell cases. The results indicate that the proposed simulation model and optimization method are accurate and efficient for the buckling analysis and optimization of a VS composite cylindrical shell. Optimization result shows that the optimum critical buckling pressure for the VS cylindrical shell is improved and is 21.1% larger than that of the constant stiffness cylindrical shell under the same geometric and boundary condition.

본 연구에서는 부식이나 보강재가 고려된 비균일한 두께를 가지는 파이프라인에 대하여 일정한 외압을 받을 때의 탄성 좌굴하중을 이론적으로 산정하였다. 길이가 매우 긴 원통형 쉘 구조물인 파이프라인을 단순한 링 구조물로 가정하였고, 고유함수를 유도하여 좌굴 임계하중을 산정하였다. 또한, 두께 변화와 두께가 감소된 구간의 범위에 따른 변수해석을 수행하였다. 이론식에 의해 산정된 좌굴 임계하중 결과를 유한요소해석 결과와 비교하여 검증하였고, 두 결과는 잘 일치함을 알 수 있었다. This paper proposes a theoretical solution of elastic critical buckling load of infinitely long pipelines with non-uniform thickness under external pressure. The non-uniform cross section of pipelines can be considered as corroded or stiffened pipelines so that this paper can be a fundamental research of pipelines that are essential technology for offshore industries. The theoretical solution of pipelines with non-uniform thickness is derived with an assumption that a cylindrical shell under external pressure can be considered as a simple ring. The eigenfunctions are derived to obtain the critical buckling load. The reduced thickness and the reduced range are considered as variables in parametric analysis. The finite element analysis is performed to verify the theoretical solutions and the results of the analytic method and the finite element method are in good agreement.

The best way to design a nuclear steam generating system to withstand seismic stresses is to establish a mathematical model, to which seismic loading can be applied, to determine the dynamic responses of the system. A practical approach for establishing such a model is to idealize the components in terms of beam elements which form the essential building blocks of the analytical model. The major shell structures of reactor vessels and steam generators are usually supported at a single elevation in the system, and are often simulated by cantilever beam elements. The use of a beam element to represent shell structure must be justified. This paper presents the results of a parametric study of thin-walled cylindrical shells which are clamped at one end while the other end is free. By using 3-D plate/shell finite element analysis, the region of application, where the beam element can reasonably simulate to shell structure, has been defiined as the combination of its geometrical parameters, e.g., the thickness/radius and length/radius. As an illustrative example, the 3-D finite element method has been used to investigate the seismic analysis of a cantilever cylindrical shell similar to the Clinch River LMFBR reactor vessel. The numerical values are compared with those produced by a beam element model. The results and conclusions obtained by this investigation can be applied to improve dynamic modeling techniques in general.

Objective To investigate effects of bone-resorptive lesion on stress distribution of femoral head and on progression in patients with osteonecrosis of the femoral head (ONFH). Methods From April 2014 to September 2018, a total of 155 femoral heads from 94 patients diagnosed with ARCO stage II and III ONFH were retrospectively reviewed, including 77 males and 17 females with aged 39.90±10.45 years old (ranged from 18-64 years). The hips were divided into two groups according to whether there were bone-resorptive lesions. Further, we compared whether there was statistical difference between the two groups in staging. Then, a case of ARCO II hip joint without bone-resorptive lesion was selected from the included patients. Six femoral head with different diameters of spherical bone-resorptive lesion of 5 mm, 7 mm, 10 mm, 14 mm, 18 mm, and 23 mm were simulated. The influence of bone-resorptive lesion on the stress distribution of necrotic area and a spherical shell extending 1 mm radially around the bone-resorptive lesion was investigated by finite element method in slow walking conditions. Results Of the 155 ONFH hips, 67 hips are complicated by bone-resorptive lesions, of which 17 were ARCO II, 50 were ARCO III. A total of 88 hips did not contain bone-resorptive lesions, of which 58 were ARCO II, ARCO III 30 cases. The proportion of ARCO stage II in the group with bone-resorptive lesions was significantly higher than that in the group without bone-resorptive lesions (χ2=25.03, P=0.000). The finite element stress distribution cloud diagram showed that there was a stress concentration area around the bone-resorptive lesions. The maximum von Mises stress around bone-resorptive lesions in the models that contained a synthetic bone-resorptive lesions were significantly higher than those reported in the matched, non-synthetic bone-resorptive lesions finite element models (t=3.139, P=0.026). The values for maximum von Mises stress around bone-resorptive lesions were 6.94±1.78 MPa and 5.01±0.35 MPa for the group with synthetic bone-resorptive lesions and the group non-synthetic bone-resorptive lesions, respectively. There was a positive correlation between the diameter of bone-resorptive lesions and the maximum and mean von Mises stress of necrotic areas as well as the maximum von Mises stress around bone-resorptive lesions. Conclusion Bone-resorptive lesions can increase the maximum stress and average stress in the necrotic area. The larger the bone-resorptive lesion, the more the stress increases. There is a stress concentration area around the bone-resorptive lesions, which may accelerate the collapse of the femoral head. Key words: Femur head necrosis; Bone resorption; Finite element analysis

Real-world groundwater modeling deals with heterogeneous and anisotropic aquifer systems. Numerical models, particularly the finite difference and finite element methods, are extensively used for modeling such a complex aquifer system. The finite difference method is an age-old straightforward approach, whereas the finite element method is more idealistic, relatively new, and has emerged as a popular approach. The unique advantages with the finite element method are (i) an irregular-shaped domain can be discretized into elements with a matching boundary, (ii) a node can be connected with the neighboring nodes in any direction. Thus, the finite element analysis allows water/solute to flow more freely toward the surrounding nodes along nodal links. On the other hand, the mathematical formulation of the finite element technique follows a set of rules step by step. Conventionally, this idealistic approach uses shape functions and integration techniques to develop element matrices, which, in turn, are assembled to form the global matrix. This conventional global matrix was found to be inconsistent with the basic partial differential equation representing the mass balance in a nodal domain as a control volume. As a result, the matrix solution, particularly for nonlinear problems (e.g., vadose zone flow, density dependent flow, and so forth) becomes unstable and computationally burdensome. To overcome the limitations of the conventional finite element method for real-world groundwater modeling, a new approach, called the direct-formulation finite element (DFFE) method, has been developed. In this approach, a two-dimensional model domain is discretized into triangular elements. Element matrices are formed directly based on flow principles and material properties of elements without using shape functions and integration process. The DFFE method is robust. The global matrix is consistent, and the solution is stable and efficient. The results obtained from this approach were found in a good agreement with that obtained from analytical and other widely used models.

Subsea oil and gas production equipment such as risers, manifolds, trees, wellheads, tubing hangers, tubing heads, blow out preventers, etc., are predominantly designed to criteria of API 6X, API 6A, API 16A, API 17D, API 17G, ASME VIII-2, ASME VIII-3, and NORSOK U-001 design codes. These industry codes provide design criteria to verify failure modes such as plastic collapse, fatigue failure, ratcheting, local strain failure, brittle failure, etc. Among these failure modes, plastic collapse and fatigue failure can be considered as the primary failure modes. A detailed review of plastic collapse design criteria from these codes and standards is discussed in this paper. These codes allow elastic (linear), limit load (elastic perfectly plastic), and elastic-plastic finite element analysis (FEA) to estimate the structural capacity. Some of these codes allow geometric nonlinearity in limit load FEA and some are not. All elastic-plastic analyses are solved with geometric nonlinearity. For this study, four components are considered which represent many subsea equipment. A pressure vessel (cylindrical shell) with internal pressure, open-end vessel (cylindrical shell) with external pressure, load shoulder, and pipe (cylindrical shell) bending are considered. Three materials with yield to tensile strength ratio of 0.53, 0.79, and 0.89 are considered in this study. A detailed review of plastic collapse criteria design criteria from these codes and standards is discussed in this paper for the four cases above.