Thermoelastic Analysis of Thick-Walled Vessels Subjected to Transient Thermal Loading

2000 ◽  
Vol 123 (1) ◽  
pp. 146-149 ◽  
Author(s):  
A. E. Segall
Keyword(s):  
Thermal Loading ◽  
Series Representation ◽  
Closed Form Solution ◽  
Thermoelastic Stress ◽  
Internal Surface ◽  
Form Solution ◽  
Element Analysis ◽  
Thermal Fields ◽  
Stress States ◽  
Transient Thermal

A closed-form solution was derived for the transient thermal fields developed in thick-walled vessels subjected to a plausible exponential heating on the internal surface with convection to the surrounding external environment. The resulting series representation of the temperature distribution as a function of time and radial position was then used to derive new relationships for the transient thermoelastic stress states. The derived expressions allow an easy analysis of the significance of the exponential terms and convective coefficient in determining the magnitudes and distribution of the resulting stress states over time. Excellent agreement was seen between the derived temperature and stress relationships and a finite element analysis when the thermophysical and thermoelastic properties were assumed to be independent of temperature.

Thermoelastic Stresses in an Axisymmetric Thick-Walled Tube Under an Arbitrary Internal Transient

2004 ◽  
Vol 126 (3) ◽  
pp. 327-332 ◽  
Author(s):  
A. E. Segall
Keyword(s):  
Thermal Loading ◽  
Series Representation ◽  
Thermoelastic Stress ◽  
Internal Surface ◽  
Stress Fields ◽  
Element Analysis ◽  
Axisymmetric Solution ◽  
Thermoelastic Stresses ◽  
Stress States ◽  
Transient Thermal

A closed-form axisymmetric solution was derived for the transient thermal-stress fields developed in thick-walled tubes subjected to an arbitrary thermal loading on the internal surface with convection to the surrounding external environment. Generalization of the temperature excitation was achieved by using a versatile polynomial composed of integral-and half-order terms. In order to avoid the difficult and potentially error prone evaluation of functions with complex arguments, Laplace transformation and a ten-term Gaver-Stehfest inversion formula were used to solve the resulting Volterra integral equation. The ensuing series representation of the temperature distribution as a function of time and radial position was then used to derive new relationships for the transient thermoelastic stress-states. Excellent agreement was seen between the derived temperature and stress relationships, existing series solutions, and a finite-element analysis when the thermophysical and thermoelastic properties were assumed to be independent of temperature. The use of a smoothed polynomial in the derived relationships allows the incorporation of empirical data not easily represented by standard functions. This in turn permits an easy analysis of the significance of the exponential boundary condition and convective coefficient in determining the magnitudes and distribution of the resulting stress states over time. Moreover, the resulting relationships are easily programmed and can be used to verify and calibrate numerical calculations.

Approximate Direct and Inverse Relationships for Thermal and Stress States in Thick-Walled Vessels Under Thermal Shock

2006 ◽  
Vol 129 (1) ◽  
pp. 52-57 ◽  
Author(s):  
A. E. Segall ◽  
R. Akarapu
Keyword(s):  
Finite Element ◽  
Thermal Shock ◽  
Thermal Loading ◽  
Thermoelastic Stress ◽  
Internal Surface ◽  
Approximate Solutions ◽  
Stress Distributions ◽  
Starting Point ◽  
Laplace Transformations ◽  
Stress States

Approximate solutions were derived for the transient through steady-state thermal-stress fields developed in thick-walled vessels subjected to a potentially arbitrary thermal shock. In order to accomplish this, Duhamel’s integral was first used to relate the arbitrary thermal loading to a previously derived unit kernel for tubular geometries. Approximate rules for direct and inverse Laplace transformations were then used to modify the resulting Volterra equation to an algebraically solvable and relatively simple form. The desired thermoelastic stress distributions were then determined using the calculated thermal states and elasticity theory. Good agreement was seen between the derived temperature and stress relationships and earlier analytical and finite-element studies of a cylinder subjected to an asymptotic exponential heating on the internal surface with convection to the outer environment. It was also demonstrated that the derived relationships can be used to approximate the more difficult inverse (deconvolution) thermal problem for both exponential (monotonic) and triangular (non-monotonic) load histories. The use of polynomial of powers tn∕2 demonstrated the feasibility of employing the method with empirical data that may not be easily represented by standard functions. For any of the direct and inverse cases explored, the resulting relationships can be used to verify, calibrate, and/or determine a starting point for finite-element or other numerical methods.

Effect of temperature variation on the plate-end debonding of FRP-strengthened beams: A theoretical study

2021 ◽  
pp. 136943322110463
Author(s):  
Dong Guo ◽  
Wan-Yang Gao ◽  
Dilum Fernando ◽  
Jian-Guo Dai
Keyword(s):  
Temperature Variation ◽  
Thermal Loading ◽  
Closed Form Solution ◽  
Form Solution ◽  
Effect Of Temperature ◽  
Shear Stresses ◽  
Limited Information ◽  
Element Analysis ◽  
Bond Slip ◽  
Loading Effects

Steel/concrete structures strengthened with externally bonded FRP plates may be subjected to significant temperature variations during their service time. Such temperature variation (i.e., thermal loading) may significantly influence the debonding mechanism in FRP-strengthened structures due to the thermal incompatibility between the FRP plate and the substrate as well as the temperature-induced bond degradation at the FRP-to-steel/concrete interface. However, limited information is available on the effect of temperature variation on the debonding failure in FRP-strengthened beams. This paper presents a new and closed-form solution to investigate the plate-end debonding failure of the FRP-strengthened beam subjected to combined thermal and mechanical (i.e., flexural) loading. A bilinear bond-slip model is used to describe the bond behavior of the FRP-to-substrate interface. The analytical solution is validated through comparisons with finite element analysis results regarding the distributions of the interfacial shear stresses, the interfacial slips and the axial stresses of the FRP plate. Given that a constant bond-slip relationship is adopted, it is observed that an increase in service temperature will lead to an increased interfacial slip at the plate end and consequently a reduced plate-end debonding load, and vice versa. Further parametric studies have indicated that the thermal loading effects become more significant when shorter and stiffer FRP plates are applied for strengthening.

scholarly journals Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

2002 ◽  
Author(s):  
P.-S. Lam ◽  
Y. J. Chao ◽  
X.-K. Zhu ◽  
Y. Kim ◽  
R. L. Sindelar
Keyword(s):  
Carbon Steel ◽  
Test Data ◽  
Storage Tank ◽  
Closed Form Solution ◽  
Crack Tip ◽  
Form Solution ◽  
Fracture Parameter ◽  
Element Analysis ◽  
Crack Tip Constraint ◽  
Senb Specimen

Mechanical testing of A285 carbon steel, a storage tank material, was performed to develop fracture properties based on the constraint theory of fracture mechanics. A series of single edge-notched bend (SENB) specimen designs with various levels of crack tip constraint were used. The variation of crack tip constraint was achieved by changing the ratio of the initial crack length to the specimen depth. The test data show that the J-R curves are specimen-design-dependent, which is known as the constraint effect. A two-parameter fracture methodology is adopted to construct a constraint-modified J-R curve, which is a function of the constraint parameter, A2, while J remains the loading parameter. This additional fracture parameter is derived from a closed form solution and can be extracted from the finite element analysis for a specific crack configuration. Using this set of SENB test data, a mathematical expression representing a family of the J-R curves for A285 carbon steel can be developed. It is shown that the predicted J-R curves match well with the SENB data over an extensive amount of crack growth. In addition, this expression is used to predict the J-R curve of a compact tension specimen (CT), and reasonable agreement to the actual test data is achieved. To demonstrate its application in a flaw stability evaluation, a generic A285 storage tank with a postulated axial flaw is used. For a flaw length of 10% of the tank height, the predicted J-R curve is found to be similar to that for a SENB specimen with a short notch, which is in a state of low constraint. This implies that the use of a J-R curve from the ASTM (American Society for Testing and Materials) standard designs, which typically are high constraint specimens, may be overly conservative for analysis of fracture resistance of large structures.

Finite Element Analysis of a Gasketed Flange Joint Under Combined Internal Pressure and Thermal Transient Loading

2007 ◽  
Author(s):  
Muhammad Abid ◽  
Javed A. Chattha ◽  
Kamran A. Khan
Keyword(s):  
Finite Element Analysis ◽  
Steady State ◽  
Internal Pressure ◽  
Thermal Loading ◽  
Flange Joint ◽  
Element Analysis ◽  
Transient Loading ◽  
Thermal Transient ◽  
Transient Thermal ◽  
Bolted Flange

Performance of a bolted flange joint is characterized mainly by its ‘strength’ and ‘sealing capability’. A number of analytical and experimental studies have been conducted to study these characteristics only under internal pressure loading. In the available published work, thermal behavior of the pipe flange joints is discussed under steady state loading with and without internal pressure and under transient loading condition without internal pressure. The present design codes also do not address the effects of steady state and thermal transient loading on the structural integrity and sealing ability. It is realized that due to the ignorance of any applied transient thermal loading, the optimized performance of the bolted flange joint can not be achieved. In this paper, in order to investigate gasketed joint’s performance i.e. joint strength and sealing capability under combined internal pressure and transient thermal loading, an extensive nonlinear finite element analysis is carried out and its behavior is discussed.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Isaiah Ramos ◽  
Young Ho Park ◽  
Jordan Ulibarri-Sanchez
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Structural Damage ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Analytical Results ◽  
Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

scholarly journals Displacement Formulations for Deformation and Vibration of Elastic Circular Torus

2021 ◽  
Author(s):  
bohua sun
Keyword(s):  
Free Vibration ◽  
Gaussian Curvature ◽  
Turning Point ◽  
Closed Form Solution ◽  
Complex Form ◽  
Form Solution ◽  
Element Analysis ◽  
Displacement Boundary ◽  
Engineering Mechanics ◽  
Maple Code

The formulation used by most of the studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of a torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will carry on my previous work [ B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of my own maple code, I am able to simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of a torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency. One of the most intestine discovery is that the crowns of a torus are the turning point of the Gaussian curvature at the crown where the mechanics' response of inner and outer torus is almost separated.

Strengthening of wide-flange columns under load

1990 ◽  
Vol 17 (5) ◽  
pp. 835-843 ◽  
Author(s):  
H. Marzouk ◽  
S. Mohan
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Critical Load ◽  
Closed Form Solution ◽  
Welding Process ◽  
Form Solution ◽  
Element Analysis ◽  
Welding Stress ◽  
Existing Structures ◽  
Welding Sequence

The present work deals with formulation of theoretical and analytical methods leading to the development of column strength curves. The formulations were developed for both elastic and inelastic behaviour. Two types of reinforcement have been developed for strengthening the W-shape columns under load. Since the column strength curves are based in part on the magnitude and distribution of residual stresses, it is extremely important to consider the new pattern of residual stresses due to welding process. Also, the welding sequence will affect the magnitude and distribution of residual stresses. Theoretical formulations leading to a closed-form solution for the prediction of critical load were developed for two types of strengthening using the superposition of original residual, new welding, and initial loading stresses. A nonlinear finite element analysis based on the large deformation theory of stability was used to predict the strengthened column critical load. It takes into consideration the effect of cooling residual stresses and new welding residual stresses. The formulations were incorporated with gradual penetration of yielding, the spreading of inelastic zones along the member length, the presence of residual stresses, and strain hardening of the material. Experiments were carried out to determine the actual capacity of strengthened columns. Seven specimens were tested using two and four strengthening plates. The welding stresses were measured through a series of experiments, and it was found that the parabolic distribution is a very close approximation to the actual new welding stress distribution. Key words: reinforcement of steel columns, welding stresses, welding sequence, strengthening of existing structures, buckling, steel plating, finite element.

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