Non-uniform Internal Pressure Research Articles

Analytical and numerical predictions of elastoplastic buckling behaviors of the subsea lined pipelines with ovality defects under hydrostatic pressure

The subsea pipelines may deteriorate and/or be cracked after a long period of service. A cost-effective trenchless rehabilitation technology is to install a thin-walled steel liner inside the pipelines. However, elliptical defects may occur in the liner due to issues such as insufficient inflation, deformation of the host pipelines, and joint misalignment in practical engineering. Thus, this study aims to develop a systematic analytical model and numerical model for the elastic and inelastic buckling behaviors of the thin-walled oval steel liner, respectively. An admissible radial displacement function is introduced to describe the single-lobe deformation of the liner. The governing equations are established to trace the equilibrium paths by applying the theory of thin-walled shells and the principle of minimum potential energy. A two-dimensional finite element model is developed for the elastic and inelastic buckling performance of the liner. The analytical solutions of elastic buckling are in good agreement with other closed-form solutions, numerical results, and respective test results available in the literature. Finally, parametric evaluations are carried out in terms of ovality, non-uniform liner-pipeline gap, internal pressure, and liner yield strength.

Simulating plate and shell structures with anisotropic resolution using adaptive smoothed particle hydrodynamics

When simulating plate and shell structures characterized by large aspect ratios, reduced-dimensional models are frequently employed due to their notable reduction in computational overhead in contrast to traditional isotropic full-dimensional models. However, in scenarios involving variations in the thickness direction, where adequate resolution in this dimension is required, reduced-dimensional models exhibit limitations. To capture variations in the thickness direction while simultaneously mitigating computational costs, an anisotropic full-dimensional model, integrated with an adaptive smoothed particle hydrodynamics method (ASPH), is developed for simulating behaviors of plate and shell structures in this study. The correction matrix, which is applied to ensure the first-order consistency, is modified accordingly by incorporating the nonisotropic kernel into it within the total Lagrangian framework of ASPH. A series of numerical examples, along with a specific application concerning the deformation of a porous film due to nonuniform internal fluid pressure in the thickness direction, are conducted to assess the computational accuracy and efficiency of the proposed ASPH method. Comparative analyses of our results against reference data and traditional isotropic SPH solutions demonstrate close agreements, affirming the suitability of the present ASPH method across various scenarios.

Study on non-uniform internal pressure distribution of twin-screw refrigeration compressor

To achieve higher efficiency of twin-screw compressors for refrigeration, the non-uniform internal pressure distribution in the rotor chamber and the flat section in the p-θ diagram were investigated in this paper. A three-dimensional CFD model of a twin-screw refrigeration compressor for chillers was established to analyze the generating mechanism of the flat section in the p-θ diagram. The p-θ diagrams of the compressor were compared under different rotational speeds and working fluids. Analysis results showed that the flat section in the p-θ diagram is caused by the periodic pressure wave propagation and reflection along the working chamber, and the pressure along the chamber is non-uniform when the sound speed is relatively slow compared with the chamber length in one compression cycle. A dimensionless ratio of chamber length and pressure wave travel distance is proposed to estimate the pressure distribution in the working chamber, based on which the flat section is prone to appear in large-scale compressors with low sound speed refrigerants like R134a. Some improvement directions were put forward to avoid efficiency losses, i.e., appropriately delaying the suction end angle and modifying the discharge port to match the pressure distribution.

Mechanical and hemodynamic responses of breast tissue under mammographic-like compression during functional dynamic optical imaging.

Studying tissue hemodynamics following breast compression has the potential to reveal new contrast mechanisms for evaluating breast cancer. However, how compression will be distributed and, consequently, how hemodynamics will be altered inside the compressed breast remain unclear. To explore the effect of compression, 12 healthy volunteers were studied by applying a step compression increase (4.5-53.4 N) using an optical imaging system capable of concurrently measuring pressure distribution and hemodynamic responses. Finite element analysis was used to predict the distribution of internal fluid pressure (IFP) in breast models. Comparisons between the measured pressure distribution and the reconstructed hemodynamic images for the healthy volunteers indicated significant (p < 0.05) negative correlations. The findings from a breast cancer patient showed that IFP distribution during compression strongly correlates with the observed differential hemodynamic images. We concluded that dynamic breast compression results in non-uniform internal pressure distribution throughout the breast that could potentially drive directed blood flow. The encouraging results obtained highlight the promise of developing dynamic optical imaging biomarkers for breast cancer by interpreting differential hemodynamic images of breast tissue during compression in the context of measured pressure distribution and predicted IFP.

An approximate analytical solution for hydraulic fracture opening under non-uniform internal pressure

An approximate analytical solution for hydraulic fracture opening under non-uniform internal pressure

Nonlinear analytical solution of nearly incompressible hyperelastic cylinder with variable thickness under non-uniform pressure by perturbation technique

In this paper, nonlinear analytical solution of pressurized thick cylindrical shells with variable thickness made of hyperelastic materials is presented. The governing equilibrium equations for the cylindrical shell with variable thickness under non-uniform internal pressure are derived based on first-order shear deformation theory (FSDT). The shell is assumed to be made of isotropic and homogenous hyperelastic material in nearly incompressible condition. Two-term Mooney-Rivlin type material is considered which is a suitable hyperelastic model for rubbers. Boundary Layer Method of the perturbation theory which is known as Match Asymptotic Expansion (MAE) is used for solving the governing equations. In order to validate the results of the current analytical solution in analyzing pressurized hyperelastic thick cylinder with variable thickness, a numerical solution based on Finite Element Method (FEM) have been investigated. Afterwards, for a rubber case study, displacements, stresses and hydrostatic pressure distribution resulting from MAE and FEM solution have been presented. Furthermore, the effects of geometry, loading, material properties and incompressibility parameter have been studied. Considering the applicability of the rubber elasticity theory to aortic soft tissues such as elastin, the behaviour of blood vessels under non-uniform pressure distribution has been investigated. The results prove the effectiveness of FSDT and MAE combination to derive and solve the governing equations of nonlinear problems such as nearly incompressible hyperelastic shells.

Second order shear deformation theory for functionally graded axisymmetric thick shell with variable thickness under non-uniform pressure

This paper studies Second order Shear Deformation Theory (SSDT), as a higher order shear deformation theory, for an axisymmetric functionally graded shell of revolution with variable thickness. According to symmetrical condition, there is not any displacement and any variation along the symmetric direction. The governing equations of proposed shell are derived by virtual work principle. As a special case, the governing equations are rewritten for a cylinder with variable thickness and non-uniform internal pressure. The comparison between current work, classical theory and First order Shear Deformation Theory (FSDT) are illustrated with some numerical results. Non-homogenous material, boundary condition effects, non-uniform pressure, arbitrary curvature with variable thickness and nonlinear displacement field are some advantages of current work. The optimum design of shell is the main goal of current approach that has a wide industrial application like aerospace engineering.

Numerical evaluation of an autofrettaged thick-walled cylinder under dynamically applied axially non-uniform internal service pressure distribution

Abstract A dynamical moving pressure structural numerical calculation model using the internal ballistics calculation pressure-time results was constituted and the vicinity of the internal ballistics and quasi-internal ballistics structural model was checked. The Von Mises stresses obtained by the dynamical structural numerical model calculations and the Von Mises stresses calculated from the shot test strain measurements were compared. The difference for the worse case was 20% and for the best case was 0.1%. Furthermore, the model gave better agreement for the higher charge masses. The numerical structural quasi-internal ballistics computation model created was verified for the top charge mass which represents the highest stress condition and used in a gun barrel design.

Approximate stress intensity factors for a semi-circular crack in an arbitrary structure under arbitrary mode I loading

Approximate Stress Intensity Factors (SIFs) for a semi-circular surface crack in arbitrary elastic finite and infinite bodies are presented. Utilizing General Point Load Weight Function (GPLWF) concept, an explicit expression is derived to determine SIFs for semi-circular cracks subjected to uniform, linear, and nonlinear loads. The presented formulation not only provides a solution for cracked bodies subjected to arbitrary two-dimensional stress distribution on the crack faces, but also could present SIFs for any point on the crack front. The results of the presented formulation for special cases, i.e. semi-circular cracks in a finite thickness plate subjected to complicated loadings, central and non-central semi-circular cracks in finite-length thick-walled cylinders subjected to a uniform internal pressure, and central semi-circular cracks in an infinite-length thick-walled cylinder subjected to a non-uniform internal pressure are compared with the available results in the literature and those obtained through FEM, indicating a very good accuracy. The proposed procedure will be generalized for semi-elliptical cracks in arbitrary structures and mixed mode loading in future.

Thermomechanical Creep Analysis of FGM Thick Cylindrical Pressure Vessels with Variable Thickness

In the present study, a theoretical solution for thermomechanical creep analysis of functionally graded (FG) thick cylindrical pressure vessel with variable thickness based on the first-order shear deformation theory (FSDT) and multilayer method (MLM) is presented. To the best of the researchers’ knowledge, in the literature, there is no study carried out into FSDT and MLM for creep response of cylindrical pressure vessels with variable thickness under thermal and mechanical loadings. The vessel is subjected to a temperature gradient and nonuniform internal pressure. All mechanical and thermal properties except Poisson’s ratio are assumed to vary along the thickness direction based on a power-law function. The thermomechanical creep response of the material is described by Norton’s law. The virtual work principle is applied to extract the nonhomogeneous differential equations system with variable coefficients. Using the MLM, this differential equations system is converted into a system of differential equations with constant coefficients. These set of differential equations are solved analytically by applying boundary and continuity conditions between the layers. In order to verify the results of this study, the finite element method (FEM) has been used and according to the results, good agreement has been achieved. It can be concluded that the temperature gradient has significant influence on the creep responses of FG thick cylindrical pressure vessel.

Time-dependent creep analysis and life assessment of 304 L austenitic stainless steel thick pressurized truncated conical shells

This paper presents a semi-analytical solution for the creep analysis and life assessment of 304L austenitic stainless steel thick truncated conical shells using multilayered method based on the first order shear deformation theory (FSDT). The cone is subjected to the non-uniform internal pressure and temperature gradient. Damages are obtained in thick truncated conical shell using Robinson's linear life fraction damage rule, and time to rupture and remaining life assessment is determined by Larson-Miller Parameter (LMP). The creep response of the material is described by Norton's law. In the multilayer method, the truncated cone is divided into n homogeneous disks, and n sets of differential equations with constant coefficients. This set of equations is solved analytically by applying boundary and continuity conditions between the layers. The results obtained analytically have been compared with the numerical results of the finite element method. The results show that the multilayered method based on FSDT has an acceptable amount of accuracy when one wants to obtain radial displacement, radial, circumferential and shear stresses. It is shown that non-uniform pressure has significant influences on the creep damages and remaining life of the truncated cone.

Time-Dependent Thermomechanical Creep Behavior of FGM Thick Hollow Cylindrical Shells Under Non-Uniform Internal Pressure

In this paper, a theoretical solution for time-dependent thermo-elastic creep analysis of a functionally graded (FG) thick-walled cylinder based on the first-order shear deformation theory is presented. The cylinder is subjected to the non-uniform internal pressure and distributed temperature field due to steady-state heat conduction from inner to outer surface of the cylinder. Mechanical and thermal properties except Poisson’s ratio are assumed to vary along the thickness direction based on a power function. The creep constitutive model is on the basis of the Norton’s law. The effects of the temperature gradient and FG grading index on the creep stresses of the cylinder are investigated. A numerical solution using finite element method is also presented and good agreement was found. Although previous publications presented analytical solutions for creep analysis of thick-walled cylindrical pressure vessels under uniform pressure, to the best of the authors’ knowledge, so far, no analytical solution has been provided for time-dependent creep analysis of FG cylinder under non-uniform internal pressure. The results of this study are applicable for designing optimum FG thick-walled cylinder.

An approach for optimization of the wall thickness (weight) of a thick-walled cylinder under axially non-uniform internal service pressure distribution

Abstract Today, improving the weight/load carrying capacity ratio of a part is the matter of studies in most of the scientific and industrial areas. Autofrettage dimensions, the amount of material removed from outer and inner radius while manufacturing and the service pressure applied affect the residual stress distribution throughout the wall thickness and hence the load-bearing capacity of a thick-walled cylinder. Calculation of residual stresses after autofrettage process and optimization of autofrettage outline dimensions by using the amount of service pressures applied are common issues in literature. In this study, mandrel-cylinder tube interference dimensions were renovated by using traditional methods for swage autofrettage process of a gun barrel. Also, the residual stresses in the cylinder after autofrettage process, inside and outside material removal process and the variable service pressure throughout the cylinder applied were taken into consideration and incorporated into the design. By using the constrained optimization method, wall thickness (thus the weight) was optimized (minimized) to achieve the specified safety factor along the length of the cylinder. For the same cylinder, the results of the suggested analytical/with residual stress calculation approach were compared to analytical/without residual stress calculation results and numerical topology optimization method calculation results. Since the experimental measurement results are not yet available, it was not possible to compare them with the calculation results. The suggested approach enabled 22.9% extra weight reduction in proportion to numerical topology optimization and enabled 4.2% extra weight reduction in proportion to analytical/without residual stress optimization. Using this approach, the gain from residual stresses after autofrettage operation, the loss of residual stresses after material removal, and the effects of service pressures can be taken into account for each stage of design.

Three-dimensional magneto-thermo-elastic analysis of functionally graded cylindrical shell

The present paper presents the three-dimensional magneto-thermo-elastic analysis of the functionally graded cylindrical shell immersed in applied thermal and magnetic fields under non-uniform internal pressure. The inhomogeneity of the shell is assumed to vary along the radial direction according to a power law function, whereas Poisson’s ratio is supposed to be constant through the thickness. The existing equations in terms of the displacement components, temperature, and magnetic parameters are derived, and then the effective differential quadrature method (DQM) is used to acquire the analytical solution. Based on the DQM, the governing heat differential equations and edge boundary conditions are transformed into algebraic equations, and discretized in the series form. The effects of the gradient index and rapid temperature on the displacement, stress components, temperature, and induced magnetic field are graphically illustrated. The fast convergence of the method is demonstrated and compared with the results obtained by the finite element method (FEM).

Fast procedure for Non-uniform optimum design of stiffened shells under buckling constraint

For tailoring the non-uniform axial compression, each sub-panel of stiffened shells should be designed separately to achieve a high load-carrying efficiency. Motivated by the challenge caused by numerous variables and high computational cost, a fast procedure for the minimum weight design of non-uniform stiffened shells under buckling constraint is proposed, which decomposes a hyper multi-dimensional problem into a hierarchical optimization with two levels. To facilitate the post-buckling optimization, an efficient equivalent analysis model of stiffened shells is developed based on the Numerical Implementation of Asymptotic Homogenization Method. In particular, the effects of non-uniform load, internal pressure and geometric imperfections are taken into account during the optimization. Finally, a typical fuel tank of launch vehicle is utilized to demonstrate the effectiveness of the proposed procedure, and detailed comparison with other optimization methodologies is made.

Eccentric annular crack under general nonuniform internal pressure

AbstractFor a better approximation of ring-shaped and toroidal cracks, a new eccentric annular crack model is proposed and an analytical approach for determination of the corresponding stress intensity factors is given. The crack is subjected to arbitrary mode I loading. A rigorous solution is provided by mapping the eccentric annular crack to a concentric annular crack. The analysis leads to two decoupled Fredholm integral equations of the second kind. For the sake of verification, the problem of a conventional annular crack is examined. Furthermore, for various crack configurations of an eccentric annular crack under uniform tension, the stress intensity factors pertaining to the inner and outer crack edges are delineated in dimensionless plots.

Instability analysis of free deformation zone of cylindrical parts based on hot-granule medium-pressure forming technology

The cylindrical part of sheet metal based on hot-granule medium-pressure forming (HGMF) technology was investigated. The stress functions of the free deformation zone and the fracture instability theory were combined to establish the analytical expression of the critical pressure of punch. The results show that the active friction between the granule medium and the sheet metal, as well as the non-uniform internal pressure presented by the solid granule medium, can obviously improve the forming performance of the sheet metal. The critical pressure of punch increases with the increment of the friction coefficient between the granule medium and sheet metal, as well as the plastic strain ratio, whereas it decreases with the increase of the material-hardening exponent. Furthermore, the impact on the critical pressure from high to low order is the plastic strain ratio, the friction coefficient, and material-hardening exponent. The deep-drawing experiment with HGMF technology on AZ31B magnesium alloy sheet verified the instability theory.

Nonlinear Dynamic Responses of Longitudinally Corrugated Shell Under Axially Nonuniform Internal Pressure

Longitudinally corrugated shell structure is an appropriate structural element adopted in aerospace, mechanical, naval, nuclear, and weapons engineering. In the present paper, the dynamic expansion of a longitudinally corrugated shell under nonuniform internal pressure with the restriction of outside rigid bodies was studied with an efficient numerical method without element discretization along the circumferential direction. Furthermore, based on the developed numerical methodology, the authors conducted intensive investigations on the geometric parameters of the corrugated shell and revealed a characteristic configuration parameter that governs the expansion dynamics of the longitudinally corrugated shell. In addition, the type (distribution) and rate of the load, which are other important factors that can influence the dynamic behavior of the corrugated shell, are also discussed. The high computational efficiency of the algorithm and the characteristic deformation behavior of the corrugated shell revealed by our analysis make the present method more favorable than commercial software in treating the expansion system in the engineering field.

Damage zone propagation and support pressure estimation around two access tunnels of the Barapukuria coalmine in Bangladesh: a two-dimensional numerical modeling approach

&lt;p&gt;The present study uses a two-dimensional boundary element method (BEM) numerical analysis to predict damage zone propagation associated with the required support pressure estimation around the two access tunnels of Barapukuria coalmine in northwest Bangladesh. Two tunnels at different depths are presented here. The stability of the two tunnels that was driven through the weak rocks' strata of Gondwana formation is examined at depths below the surface 290 m and 453 m. The two tunnels involve horseshoe-shaped design. The shallower tunnels, which are located below the surface 290 m, are presented by model A. The deeper tunnels, which are located below the surface 453 m, are presented by model B. Both tunnels are horseshoe-shaped with a height and span of about 4.5 m and 4 m, respectively. The modeling analysis was carried out in two stages to predict the damage zone and required support pressure. The first stage considered the model without support installation. The second stage measured the model with non-uniform internal support pressure installation. It is reasonable to mention that prior and subsequent to the support pressure estimation, three important parameters, like- strength factor, failure trajectories, and deformation boundaries in the vicinity of the two tunnels have been computed properly. Final results reveal that the strength factor values ranged from 0.33 to 0.99 would create the intense deformation at the roof and sidewalls. The damage zone would be extended from 0.64 to 0.74 m towards the roof and sidewalls. The damage zone would be ranged from 1.95 to 2.21 m, for shallower and deeper tunnels, respectively. For shallower tunnels, the required support pressure would be ranged from 4.0 to 9.0 MPa. For deeper tunnels, the essential support pressure would be ranged from 7.0 to 14 MPa.&lt;/p&gt;

Three-dimensional Magneto-thermo-elastic Analysis of Functionally Graded Truncated Conical Shells

This work deals with the three-dimensional magneto-thermo -elastic problem of a functionally graded truncated conical shell under non-uniform internal pressure subjected to magnetic and thermal fields. The material properties are assumed to obey the power law form that depends on the thickness coordinate of the shell. The formulation of the problem begins with the derivation of fundamental relations of thermo-elasti city in the conical coordinate system. Subsequently, the differential quadrature method (DQM) is employed to discretize the resulting differential equations and transform them into a system of algebraic equations. Numerical results are presented to illustrated effects of nonhomogeneity properties of material and thermal loads on the distributions of displacement, stress, temperature and induced magnetic fields. Finite element method is used to validate the results of DQM for a functionally graded truncated conical shell which shows excellent agreement.