scholarly journals Thermoelastic Closed-Form Solutions of FGM Plates Subjected to Temperature Change in Axial and Thickness Directions

2020 ◽  
Author(s):  
Yen-Ling Chung
Keyword(s):  
Closed Form ◽  
Temperature Change ◽  
Axial Force ◽  
Maximum Stress ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Bottom Surface ◽  
Thermal Loads ◽  
Element Analysis ◽  
Closed Form Solutions

Abstract An analytical solution of simply supported FGM plates under thermal loads is developed based on medium-thick plate assumption. Further to assume constant Poisson’s ratio and thermal expansion coefficient, the closed-form solutions of the FGM plates with through-the-thickness Young’s modulus under temperature change in x - and z -directions are evaluated, expressed in terms of the thermal axial force and thermal bending moment. The closed-form solutions confirmed by finite element analysis give a complete insight into the thermal-mechanical behavior of FGM plates. Hence, the deflection, strain, stress, axial force, and bending moment of the FGM plate under thermal loads in axial and thickness directions are discussed. Results show that the use of FGM makes the maximum stress from the top or bottom surface move to the inner portion of the FGM plate, and significantly reduces the maximum stress of the plates. Moreover, although the FGM plate is subjected to thermal load in the thickness direction, the deflection of the FGM plate can be zero by properly choosing the steep material gradation, directly derived from the obtained closed-form solution.

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.

Determination of Pipe Whip Restraint Location to Prevent Plastic Hinge Formation in High Energy Piping Systems

2011 ◽  
Author(s):  
Sivadol Vongmongkol ◽  
Asgar Faal-Amiri ◽  
Hari M. Srivastava
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Power Plants ◽  
Plastic Hinge ◽  
Bending Moment ◽  
High Energy ◽  
Piping System ◽  
Secondary Effects ◽  
Element Analysis ◽  
Closed Form Solutions

The purpose of this study is to determine the Pipe Whip Restraint (PWR) location that would prevent the formation of a plastic hinge due to secondary effects of a postulated pipe break load in a high energy line(1). The prevention of a plastic hinge formation at the PWR location is important since its secondary effects could lead to additional interactions with safety related equipment, structure, and component that are essential to safely shutdown the nuclear power plants. The proper location of the PWR can be found by using the relationship between bending moment-carrying capacity of the pipe and the applied thrust force. Several closed-form solutions obtained from several literatures were studied and used to calculate bending moment-carrying capacities of a piping system and ultimately used to determine a plastic hinge length. The plastic hinge formation is also determined analytically by using the Finite Element Analysis (FEA) method. ANSYS LS-DYNA® [8] Explicit Finite Element code is used in modeling the pipe whip models, which includes the piping system and pipe whip restraint. Comparisons are made between the analytical (FEA) results and the results from several closed-form solutions.

The Effect of Compressibility on the Stress Distributions in Thin Elastomeric Blocks and Annular Bushings

1992 ◽  
Vol 59 (4) ◽  
pp. 902-908 ◽  
Author(s):  
Yeh-Hung Lai ◽  
D. A. Dillard ◽  
J. S. Thornton
Keyword(s):  
Finite Element Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stress Distributions ◽  
Element Analysis ◽  
Shape Factors ◽  
Closed Form Solutions ◽  
Apparent Stiffness ◽  
Bulk Compressibility

The effect of the bulk compressibility of elastomers on the response of rubber blocks and bushings bonded to platens is in vestigated. Closed-form solutions for the stresses and deformations within the elastomer are presented for the case of rigid adherends. It is shown that even with relatively small shape factors, the compressibility can significantly affect the apparent stiffness. A finite element analysis shows that the closed-form solution accurately predicts the stress distribution for rigid adherends, but also reveals that platen deformations in realistic systems may significantly alter the distributions.

An Improved Closed-Form Solution for Shearing and Peeling Stresses of Trimaterial Assembly in Electronic Packaging

2008 ◽  
Vol 5 (1) ◽  
pp. 36-42 ◽  
Author(s):  
D. Sujan ◽  
M.V.V. Murthy ◽  
A.Y. Hassan ◽  
K.N. Seetharamu
Keyword(s):  
Numerical Simulation ◽  
Closed Form ◽  
Temperature Change ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stress Model ◽  
Shearing Stress ◽  
Uniform Temperature ◽  
Applied Physics ◽  
Closed Form Solutions

Closed-form solutions for shearing and peeling stresses of trimaterial assembly were initially provided by Schmidt in 1999 [1] and Suhir in 2001 [2]. However, there exist some contradictions and inconsistencies the solutions of both Schmidt and Suhir. The contradiction arises in consideration of the exponent parameter k in the characteristic equation. Both Schmidt and Suhir showed that the exponent parameter k in the shearing stresses contains two roots, but for both cases they considered only one root for k; as a consequence, it leads to a mathematical inconsistency in the solution. In the present paper, a model for shearing stress for uniform temperature change is presented that considers both roots for k. Subsequently, a model for peeling stress is presented that considers moment equilibrium combined with the improved shearing stress model described above. The contradictions in Schmidt's and Suhir's solutions are highlighted in this paper. Analytical and FEM solutions are presented for the same trimaterial package as used by Suhir (cf. Journal of Applied Physics, ibid.) for comparison. The improved analytical results and the numerical simulation indicate better agreement compared with the solutions provided by Schmidt and Suhir.

Closed-form moment-curvature relations for reinforced concrete cross sections under bending moment and axial force

2016 ◽  
Vol 129 ◽  
pp. 67-80 ◽  
Author(s):  
Pedro Dias Simão ◽  
Helena Barros ◽  
Carla Costa Ferreira ◽  
Tatiana Marques
Keyword(s):  
Reinforced Concrete ◽  
Closed Form ◽  
Axial Force ◽  
Cross Sections ◽  
Bending Moment

Preliminary Parametric Assessment of a Bolted Endplate Joint under Combined Axial Force and Cyclic Bending Moment

2011 ◽  
Vol 255-260 ◽  
pp. 718-721
Author(s):  
Z.Y. Wang ◽  
Q.Y. Wang
Keyword(s):  
Finite Element Analysis ◽  
Axial Force ◽  
Seismic Design ◽  
Axial Load ◽  
Failure Modes ◽  
Bending Moment ◽  
Element Analysis ◽  
Cyclic Behaviour ◽  
Joint Behaviour ◽  
Steel Joints

Problems regarding the combined axial force and bending moment for the behaviour of semi-rigid steel joints under service loading have been recognized in recent studies. As an extended research on the cyclic behaviour of a bolted endplate joint, this study is performed relating to the contribution of column axial force on the cyclic behaviour of the joint. Using finite element analysis, the deteriorations of the joint performance have been evaluated. The preliminary parametric study of the joint is conducted with the consideration of flexibility of the column flange. The column axial force was observed to significantly influence the joint behaviour when the bending of the column flange dominates the failure modes. The reductions of moment resistance predicted by numerical analysis have been compared with codified suggestions. Comments have been made for further consideration of the influence of column axial load in seismic design of bolted endplate joints.

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

scholarly journals A New Closed-Form Solution of the Side Abutment Pressure Distribution of Roadway

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Liang Cheng ◽  
Yidong Zhang
Keyword(s):  
Plastic Zone ◽  
Pressure Distribution ◽  
Closed Form ◽  
Abutment Pressure ◽  
Closed Form Solution ◽  
Evaluation Process ◽  
Friction Angle ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Roadway Stability

Instability of coal wall is one of the hot-button and difficult issues in the study of coal mine ground control. The shallow side coal of roadway in the coal measures is usually weak and consequently easy to bring about failure. Hence, the side abutment pressure redistributes and dramatically influences the roadway stability. Since the previous closed-form solutions of the side abutment pressure do not take into account all the necessary parameters which include the properties of the coal and the interface between coal and roof/floor, the roadway height, and the support strength, a mechanical model is established based on the equilibrium of the plastic zone, and a new closed-form solution is derived in this paper. Moreover, a numerical investigation is conducted to validate the accuracy of the closed-form solution. The numerical results of the side abutment pressure distribution are in good agreement with the closed-form solution. Afterwards, a parametric analysis of the width of the plastic zone is carried out, and the results show that the width of the plastic zone is nearly negatively linearly correlated with the friction angle and the cohesion of the coal, the interfacial cohesion, and the support strength. By contrast, it is positively linearly correlated with the roadway height and negatively exponentially correlated with the interfacial friction angle. The results obtained in the present study could be useful for the evaluation process of roadway stability.

Determination of critical angle of circumferential throughwall crack for structurally distorted 90° pipe bends under bending moment with and without internal pressure

2017 ◽  
Vol 233 (5) ◽  
pp. 817-830 ◽  
Author(s):  
S Sumesh ◽  
AR Veerappan ◽  
S Shanmugam
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Closed Form ◽  
Bending Moment ◽  
External Loading ◽  
Element Analysis ◽  
Critical Crack ◽  
Structural Distortions ◽  
Internal Pressures

Throughwall circumferential cracks (TWC) in elbows can considerably minimize its collapse load when subjected to in-plane bending moment. The existing closed-form collapse moment equations do not adequately quantify critical crack angles for structurally distorted cracked pipe bends subjected to external loading. Therefore, the present study has been conducted to examine utilizing elastic-plastic finite element analysis, the influence of structural distortions on the variation of critical TWC of 90° pipe bends under in-plane closing bending moment without and with internal pressure. With a mean radius ( r) of 50 mm, cracked pipe bends were modeled for three different wall thickness, t (for pipe ratios of r/ t = 5,10,20), each with two different bend radius, R (for bend ratios of R/r = 2,3) and with varying degrees of ovality and thinning (0 to 20% with increments of 5%). Finite element analyses were performed for two loading cases namely pure in-plane closing moment and in-plane closing bending with internal pressure. Normalized internal pressures of 0.2, 0.4, and 0.6 were applied. Results indicate the modification in the critical crack angle due to the pronounced effect of ovality compared to thinning on the plastic loads of pipe bends. From the finite element results, improved closed-form equations are proposed to evaluate plastic collapse moment of throughwall circumferential cracked pipe bends under the two loading conditions.

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