Journal articles: 'Mechanics solution'

1

Junker, G., and S. Matthiesen. "Pseudoclassical mechanics and its solution." Journal of Physics A: Mathematical and General 28, no. 5 (March 7, 1995): 1467–68. http://dx.doi.org/10.1088/0305-4470/28/5/029.

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Deng, Hong Wei, Chun Fang Dong, Jie Lin Li, Ke Ping Zhou, Wei Gang Tian, and Jian Zhang. "Experimental Study on Sandstone Freezing-Thawing Damage Properties under Condition of Water Chemistry." Applied Mechanics and Materials 608-609 (October 2014): 726–31. http://dx.doi.org/10.4028/www.scientific.net/amm.608-609.726.

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For the purpose of researching the freezing-thawing cycle pHysical mechanics properties of sandstone in various chemical solutions, taking the red sandstones from Shandong as the example, freezing-thawing cycles experiments under the condition of H2SO4 solution (pH≈1.5), NaOH solution (pH≈12.5), NaCl solution (pH≈7, mass fraction is 4%) and water were conducted. The nuclear magnetic resonance (NMR) technique was used to test the porosity of rock samples after freezing-thawing cycles. Brazilian splitting test was also conducted to test the samples with different times of freezing-thawing cycles and soaking solutions. Results show that the quality change of samples in various solutions is different. The mass of sample in water increased, however, the mass change of the sample in other three solutions showed a firstly increasing and then decreasing tendency. The porosity distribution in rock changed obviously after different time’s freezing-thawing cycles. After 30 times freezing-thawing cycles, the porosity in H2SO4 solution, NaOH solution, NaCl solution and water has increased by 151.1%, 85.443%, 39.388%, and 17.976% respectively. With the increase of freezing-thawing cycle’s times, tensile strength of the rock reduced, but the damage properties were different in various solutions. The research can provide some mechanical parameters basis to physical mechanics properties of sandstones.

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Liu, G. R., Y. G. Xu, and Z. P. Wu. "Total solution for structural mechanics problems." Computer Methods in Applied Mechanics and Engineering 191, no. 8-10 (December 2001): 989–1012. http://dx.doi.org/10.1016/s0045-7825(01)00314-0.

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SHI, XUGUANG, MING YU, and YISHI DUAN. "TOPOLOGICAL SOLUTION OF BOHMIAN QUANTUM MECHANICS." Modern Physics Letters A 24, no. 06 (February 28, 2009): 453–61. http://dx.doi.org/10.1142/s021773230902711x.

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The topological solutions of the De Broglie–Bohm quantum mechanics are presented. Starting from the Schrödinger equation for one particle system and ϕ-mapping topological current theory, the trajectory of the particle is derived explicitly, and can be used as the world line of the particle. The world line is just at the zero point of the wave function and it is shown that the vorticity of the world line can be expressed by Hopf index and Brouwer degree. The evolution of the world line at the bifurcation point is given.

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Deng, Hong Wei, Chun Fang Dong, Jie Lin Li, Ke Ping Zhou, Wei Gang Tian, and Jian Zhang. "Experimental Study on Sandstone Freezing-Thawing Damage Properties under Condition of Water Chemistry." Applied Mechanics and Materials 556-562 (May 2014): 826–32. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.826.

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For the purpose of researching the freezing-thawing cycle physical mechanics properties of sandstone in various chemical solutions, taking the red sandstones from Shandong as the example, freezing-thawing cycles experiments under the condition of H2SO4solution (pH≈1.5), NaOH solution (pH≈12.5), NaCl solution (pH≈7, mass fraction is 4%) and water were conducted. The nuclear magnetic resonance (NMR) technique was used to test the porosity of rock samples after freezing-thawing cycles. Brazilian splitting test was also conducted to test the samples with different times of freezing-thawing cycles and soaking solutions. Results show that the quality change of samples in various solutions is different. The mass of sample in water increased, however, the mass change of the sample in other three solutions showed a firstly increasing and then decreasing tendency. The porosity distribution in rock changed obviously after different time’s freezing-thawing cycles. After 30 times freezing-thawing cycles, the porosity in H2SO4solution, NaOH solution, NaCl solution and water has increased by 151.1%, 85.443%, 39.388%, and 17.976% respectively. With the increase of freezing-thawing cycle’s times, tensile strength of the rock reduced, but the damage properties were different in various solutions. The research can provide some mechanical parameters basis to physical mechanics properties of sandstones.

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Schwenninger, David, Hans-Joachim Priebe, Matthias Schneider, Hanna Runck, and Josef Guttmann. "Optical clearing: impact of optical and dielectric properties of clearing solutions on pulmonary tissue mechanics." Journal of Applied Physiology 123, no. 1 (July 1, 2017): 27–37. http://dx.doi.org/10.1152/japplphysiol.00234.2016.

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Optical clearing allows tissue visualization under preservation of organ integrity. Optical clearing of organs with a physiological change in three-dimensional geometry (such as the lung) would additionally allow visualization of macroscopic and microscopic tissue geometry. A prerequisite, however, is the preservation of the native tissue mechanics of the optically cleared lung tissue. We investigated the impact of optical and dielectric properties of clearing solutions on biomechanics and clearing potency in porcine tissue strips of healthy lungs. After fixation, bleaching, and rehydration, four methods of optical clearing were investigated using eight different protocols. The mechanical and optical properties of the cleared lung tissue strips were investigated by uniaxial tensile testing and by analyzing optical transparency and translucency for red, green, and blue light before, during, and after the biochemical optical clearing process. Fresh tissue strips were used as controls. Best balance between efficient clearing and preserved mechanics was found for clearing with a 1:1 mixture of dimethyl sulfoxide (DMSO) and aniline. Our findings show that 1) the degree of tissue transparency and translucency correlated with the refractive index of the clearing solution index ( r = 0.976, P = 0.0004; and r = 0.91, P = 0.0046, respectively), 2) tissue mechanics were affected by dehydration and the type of clearing solution, and 3) tissue biomechanics and geometry correlated with the dielectric constant of the clearing solution ( r = −0.98, P < 0.00001; and r = 0.69, P = 0.013, respectively). We show that the lower the dielectric constant of the clearing solutions, the larger the effect on tissue stiffness. This suggests that the dielectric constant is an important measure in determining the effect of a clearing solution on lung tissue biomechanics. Optimal tissue transparency requires complete tissue dehydration and a refractive index of 1.55 of the clearing solution. NEW & NOTEWORTHY Investigating optical clearing in porcine lung tissue strips, we found that refractive index and dielectric constant of the clearing solution affected tissue clearing and biomechanics. By documenting the impact of the composition of the clearing solution on clearing potency and preservation of tissue mechanics, our results help to compose optimal clearing solutions. In addition, the results allow conclusions on the molecular interaction of solvents with collagen fibers in tissue, thereby consolidating existing theories about the functionality of collagen.

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Georgiades, Fotios. "Exact Augmented Perpetual Manifolds: Corollary about Different Mechanical Systems with Exactly the Same Motions." Mathematical Problems in Engineering 2021 (September 10, 2021): 1–24. http://dx.doi.org/10.1155/2021/6031142.

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Perpetual points have been defined in mathematics recently, and they arise by setting accelerations and jerks equal to zero for nonzero velocities. The significance of perpetual points for the dynamics of mechanical systems is ongoing research. In the linear natural, unforced mechanical systems, the perpetual points form the perpetual manifolds and are associated with rigid body motions. Extending the definition of perpetual manifolds, by considering equal accelerations, in a forced mechanical system, but not necessarily zero, the solutions define the augmented perpetual manifolds. If the displacements are equal and the velocities are equal, the state space defines the exact augmented perpetual manifolds obtained under the conditions of a theorem, and a characteristic differential equation defines the solution. As a continuation of the theorem herein, a corollary proved that different mechanical systems, in the exact augmented perpetual manifolds, have the same general solution, and, in case of the same initial conditions, they have the same motion. The characteristic differential equation leads to a solution defining the augmented perpetual submanifolds and the solution of several types of characteristic differential equations derived. The theory in a few mechanical systems with numerical simulations is verified, and they are in perfect agreement. The theory developed herein is supplementing the already-developed theory of augmented perpetual manifolds, which is of high significance in mathematics, mechanics, and mechanical engineering. In mathematics, the framework for specific solutions of many degrees of freedom nonautonomous systems is defined. In mechanics/physics, the wave-particle motions are of significance. In mechanical engineering, some mechanical system’s rigid body motions without any oscillations are the ultimate ones.

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Bruno, Alexander D., and Alexander B. Batkhin. "Survey of Eight Modern Methods of Hamiltonian Mechanics." Axioms 10, no. 4 (November 4, 2021): 293. http://dx.doi.org/10.3390/axioms10040293.

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Here we describe eight new methods, arisen in the last 60 years, to study solutions of a Hamiltonian system with n degrees of freedom. The first six of them are intended for systems with small parameters or without them. The methods allow to find families of periodic solutions and families of invariant n-dimensional tori by means of analytic computation near a stationary solution, near a periodic solution and near an invariant torus, using the corresponding normal form of a Hamiltonian. Then we can continue the founded families by means of numerical computation. In a Hamiltonian system without parameters, only periodic solutions and invariant n-dimensional tori form one-parameter families. The last two methods are intended for systems with not small parameters, which do not depend on time. They allow computing sets of parameters, which guarantee the stability of some solutions for linear (method seven) and nonlinear (method eight) systems. We do not consider chaotic behaviors, but only regular ones.

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Dyka, Ewa, and Bogdan Rogowski. "Fundamental solutions in piezoelectricity. Penny-shaped crack solution." International Journal of Pressure Vessels and Piping 83, no. 7 (July 2006): 512–24. http://dx.doi.org/10.1016/j.ijpvp.2006.03.004.

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10

Petrov, I. B. "Application of grid-characteristic method for numerical solution of deformable solid mechanics dynamical problems." COMPUTATIONAL MATHEMATICS AND INFORMATION TECHNOLOGIES 1, no. 1 (2017): 1–20. http://dx.doi.org/10.23947/2587-8999-2017-1-1-1-20.

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11

Burchfield, D. M., and J. A. Rall. "Energetics and mechanics of frog skeletal muscle in hypotonic solution." American Journal of Physiology-Cell Physiology 251, no. 1 (July 1, 1986): C66—C71. http://dx.doi.org/10.1152/ajpcell.1986.251.1.c66.

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Hypotonic solutions are known to potentiate muscle force production and increase actomyosin ATPase activity in solution. As such, both the rate and amount of ATP hydrolysis should increase during contraction. This was tested indirectly by measuring force and energy liberation in Rana pipiens semitendinosus muscles at 0 degrees C in hypotonic solution. Force and the amount and rate of energy liberation increased. This increase is consistent with the interpretation that the rate of ATP hydrolysis is increased in hypotonic solution. Muscles, stretched to beyond myofilament overlap, liberate a substantial fraction of the energy liberated at maximal myofilament overlap. This energy liberation, the activation heat, is thought to reflect the energy utilized to cycle Ca2+. Hypotonic solution decreased the amplitude and the rate of the activation heat, suggesting that the amount and rate of Ca2+ cycled by the sarcoplasmic reticulum is reduced. Thus in hypotonic solution, force production and the rate of ATP hydrolysis by the cross bridges are potentiated despite an apparent decrease in Ca2+ cycling.

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12

Toro, L. A., C. A. Cardona, Yu A. Pisarenko, and A. V. Frolkova. "THE FINITE ELEMENT METHOD (FEM): AN APPLICATION TO FLUID MECHANICS AND HEAT TRANSFER." Fine Chemical Technologies 13, no. 4 (August 28, 2018): 17–25. http://dx.doi.org/10.32362/2410-6593-2018-13-4-17-25.

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In this paper the finite element method (FEM) is used to solve three problems that are of the paramount importance in Chemical Engineering. The first problem is related with the bidimensional flow of an ideal fluid around a cylindrical body, and the objective is to determine the velocity distribution of the flow. To model the flow, the potential formulation is used to obtain an analytical solution, and then, the approximated solution obtained by using FEM is compared with the analytical solution. From this comparison, it is deduced that both solutions have a good agreement. The second problem is the calculation of the temperature profile in a two-dimensional body with specified boundary conditions. This problem is modeled by the two-dimensional Laplace equation, and from the problem data and using variables separation, an analytical solution was obtained. Then, FEM was used to obtain an approximate solution and compared with analytical ones. Besides, from this comparison, it is concluded that both solutions agree. Finally, in the third problem the temperature distribution in a bidimensional body with internal heat generation is studied. This problem is modeled by Poisson equation in two dimensions, but due to the boundary conditions and the complications that arise by adding some heat sources in the final FEM discretization, the problem does not have an analytical solution. However, the analysis of FEM solution indicates that this solution is correct.

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IKEMORI, HITOSHI, SHINSAKU KITAKDO, HAJIME NAKATANI, HIDEHARU OTSU, and TOSHIRO SATO. "QUANTUM MECHANICS ON Sn AND MERON SOLUTION." Modern Physics Letters A 13, no. 01 (January 10, 1998): 15–21. http://dx.doi.org/10.1142/s0217732398000048.

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A particle in quantum mechanics on manifolds couples to the induced topological gauge field that characterizes the possible inequivalent quantizations. For instance, the gauge potential induced on S2 is that of a magnetic monopole located at the center of S2. We find that the gauge potential induced on S3(S2n+ 1) is that of a meron (generalized meron) also sitting at the center of S3(S2n+ 1).

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Bitzarakis, S., M. Papadrakakis, and A. Kotsopulos. "Parallel solution techniques in computational structural mechanics." Computer Methods in Applied Mechanics and Engineering 148, no. 1-2 (August 1997): 75–104. http://dx.doi.org/10.1016/s0045-7825(97)00028-5.

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15

Gavrilkina, M. V., V. V. Glagolev, and A. A. Markin. "Solution of one problem of fracture mechanics." Journal of Applied Mechanics and Technical Physics 48, no. 4 (July 2007): 571–76. http://dx.doi.org/10.1007/s10808-007-0072-1.

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Halama, Radim, Jiří Podešva, Ryosuke Suzuki, Masaaki Matsubara, and Rostislav Čech. "Mechanics of Herbert Pendulum Hardness Tester and its Application." Key Engineering Materials 741 (June 2017): 122–27. http://dx.doi.org/10.4028/www.scientific.net/kem.741.122.

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The knowledge of classical mechanics gives deeper insight into the Herbert hardness tester applicability for material testing. Elastic materials with low friction presence between contact surfaces are supposed to be investigated in this study. Firstly the dynamics approach is used to obtain simplified solution of swing angle. Then a new solution of the problem is gained by means of an energy approach. Slight decrease of the swing angle is predicted by the new solution as also shown in experiments. After comparison of both solutions a new formulae useful for evaluation of rolling resistance coefficient is applied for measurements performed on some metallic materials and artificial sapphire. Rolling resistance coefficients obtained by the way are always less than maximal estimated value.

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17

Zhan, Zhi Xin, Wei Ping Hu, Miao Zhang, and Qing Chun Meng. "The Fatigue Life Prediction Problem for Fixed Plate of Helicopter." Advanced Materials Research 452-453 (January 2012): 1164–68. http://dx.doi.org/10.4028/www.scientific.net/amr.452-453.1164.

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This paper analyses the fatigue life prediction problem for fixed plate of helicopter in the case of cyclic loading using damage mechanics methods. The material parameters are obtained by the results of the fatigue test of standard specimens. According to the theory of damage mechanics, the closed solution of fixed plate’s fatigue life is obtained. And the numerical solution is gotten through using finite element software ANSYS. Numerical solution, closed solutions and experimental results are consistent. This research provides a feasible way to predict the fatigue lives of structure members by means of damage mechanics.

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Shabouei, M., and K. B. Nakshatrala. "Mechanics-Based Solution Verification for Porous Media Models." Communications in Computational Physics 20, no. 5 (November 2016): 1127–62. http://dx.doi.org/10.4208/cicp.oa-2016-0007.

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AbstractThis paper presents a new approach to verify the accuracy of computational simulations. We develop mathematical theorems which can serve as robusta posteriorierror estimation techniques to identify numerical pollution, check the performance of adaptive meshes, and verify numerical solutions. We demonstrate performance of this methodology on problems from flow thorough porous media. However, one can extend it to other models. We construct mathematical properties such that the solutions to Darcy and Darcy-Brinkman equations satisfy them. The mathematical properties include the total minimum mechanical power, minimum dissipation theorem, reciprocal relation, and maximum principle for the vorticity. All the developed theorems have firm mechanical bases and are independent of numerical methods. So, these can be utilized for solution verification of finite element, finite volume, finite difference, lattice Boltzmann methods and so forth. In particular, we show that, for a given set of boundary conditions, Darcy velocity has the minimum total mechanical power of all the kinematically admissible vector fields. We also show that a similar result holds for Darcy-Brinkman velocity. We then show for a conservative body force, the Darcy and Darcy-Brinkman velocities have the minimum total dissipation among their respective kinematically admissible vector fields. Using numerical examples, we show that the minimum dissipation and total mechanical power theorems can be utilized to identify pollution errors in numerical solutions. The solutions to Darcy and Darcy-Brinkman equations are shown to satisfy a reciprocal relation, which has the potential to identify errors in the numerical implementation of boundary conditions. It is also shown that the vorticity under both steady and transient Darcy-Brinkman equations satisfy maximum principles if the body force is conservative and the permeability is homogeneous and isotropic. A discussion on the nature of vorticity under steady and transient Darcy equations is also presented. Using several numerical examples, we will demonstrate the predictive capabilities of the proposeda posterioritechniques in assessing the accuracy of numerical solutions for a general class of problems, which could involve complex domains and general computational grids.

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Rvachev, V. L., and T. I. Sheiko. "R-Functions in Boundary Value Problems in Mechanics." Applied Mechanics Reviews 48, no. 4 (April 1, 1995): 151–88. http://dx.doi.org/10.1115/1.3005099.

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Described are the concepts and applications of the R-functions theory in continuum mechanics boundary value problems which model fields of different physical natures. With R-functions there appears the possibility of creating a constructive mathematical tool which incorporates the capabilities of classical continuous analysis and logic algebra. This allows one to overcome the main obstacle which hinders the use of variational methods when solving boundary value problems in domains of complex shape with complex boundary conditions, this obstacle being connected with the construction of so-called coordinate sequences. In contrast to widely used methods of the network type (finite difference, finite and boundary elements), in the R-functions method all the geometric information present in the boundary value problem statement is reduced to analytical form, which allows one to search for a solution in the form of formulae called solution structures containing some indefinite functional components. A method of constructing solution structures satisfying the required conditions of completeness has been developed. The structural formulae include the left-hand sides of the normalized equations of the boundaries of the domains or their regions being considered, thus allowing one to change the solution structure expeditiously when changing the geometric shape. Given in the work is a definition of the basic class of R-functions, solution with their help of the inverse problem of analytical geometry (construction of equations of specified configurations); generalization of the Taylor-Hermite formulae for functional spaces in which points are represented by lines and surfaces; and construction of solution structures of some types of boundary value problems. Shown are the solutions of a number of concrete problems in these application fields with the use of the RL language and POLYE system.

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20

Nauenberg, Michael. "Quantum Mechanics and Liouville's Equation." Quanta 6, no. 1 (September 9, 2017): 53. http://dx.doi.org/10.12743/quanta.v6i1.63.

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In non-relativistic quantum mechanics, the absolute square of Schrödinger's wave function for a particle in a potential determines the probability of finding it either at a position or momentum at a given time. In classical mechanics the corresponding problem is determined by the solution of Liouville's equation for the probability density of finding the joint position and momentum of the particle at a given time. Integrating this classical solution over either one of these two variables can then be compared with the probability in quantum mechanics. For the special case that the force is a constant, it is shown analytically that for an initial Gaussian probability distribution, the solution of Liouville's integrated over momentum is equal to Schrödinger's probability function in coordinate space, provided the coordinate and momentum initial widths of this classical solution satisfy the minimal Heisenberg uncertainty relation. Likewise, integrating Lioville's solution over position is equal to Schrödinger's probability function in momentum space.Quanta 2017; 6: 53–56.

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21

Setiono, Teguh, Dena Hendriana, Henry Nasution, Gembong Baskoro, and Edi Sofyan. "Impact of Increasing Mechanic Competence through Competence Based Curriculum to Improve Product Support Performance in Leading Indonesian Heavy Equipment." Proceedings of The Conference on Management and Engineering in Industry 3, no. 3 (August 4, 2021): 62. http://dx.doi.org/10.33555/cmei.v3i3.85.

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The availability and readiness of heavy equipment depends on the level of product support. Product support as after sales service is important for customers to ensure that heavy equipment purchased is always ready for use and produces optimal production. Leadtime and mechanic speed in solving problems that occur in equipment and the so called On Time in Full Solution (OTIF Solution) affects the usability and productivity of equipment. Performance OTIF Solution affects Product Support Performance, and this affects the level of customer satisfaction. The development of mechanic competencies through competency-based training and problems in the field with reference to the Special Work Competency Standards is a strategy to increase the ability and speed of mechanics to solve problems that occur in machines in order to get good OTIF Solution performance. This research aims to determine the impact of increasing competence. mechanic through training with a competency-based curriculum on product performance support. This research was conducted by providing training with the blended learning method with training modules for machines with under-target OTIF Solution performance. The results showed that after mechanics received training, the OTIF Solution increased from the previous 2 years. namely 89% and 88% below the target of 90% to 93%.

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Haji-Sheikh, A., and M. Mashena. "Integral Solution of Diffusion Equation: Part 1—General Solution." Journal of Heat Transfer 109, no. 3 (August 1, 1987): 551–56. http://dx.doi.org/10.1115/1.3248123.

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A generalized method is presented that accommodates the linear form of the diffusion equation in regions with irregular boundaries. The region of interest many consist of subregions with spatially variable thermal properties. The solution function for the diffusion equation is decomposed into two solutions: one with homogeneous and the other with nonhomogeneous boundary conditions. The Galerkin functions are used to provide a solution for a diffusion problem with homogeneous boundary condition and linear initial condition. Problems with nonhomogeneous boundary conditions can be dealt with by many other schemes, including the standard Galerkin method. The final solution is a combination of these two solutions.

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贾, 普荣. "General Solution of Elastic Mechanics for Orthotropic Materials." International Journal of Mechanics Research 11, no. 03 (2022): 54–62. http://dx.doi.org/10.12677/ijm.2022.113007.

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Manchiryal, Ram Kishore, Basim Khidhir, and Himanshu Gaur. "Solution of structural mechanics problems by machine learning." International Journal of Hydromechatronics 1, no. 1 (2022): 1. http://dx.doi.org/10.1504/ijhm.2022.10045584.

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Dong, Wen Sheng, Zheng Lei, and Xue Mei Liu. "Solution of Material Mechanics by RPIM Meshless Method." Advanced Materials Research 740 (August 2013): 211–16. http://dx.doi.org/10.4028/www.scientific.net/amr.740.211.

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With the compact support of radial point interpolation shape functions (RPIM), the stiffness matrix of system equation can be sparse, so its very suitable for meshless methods.This interpolation method have the Kronecker delta function property, so the essential boundary conditions can be enforced directly and accurately without any additional treatment. In this paper, the radial point interpolation shape function is used, calculate the shape function in different node distribution cases, analyse the compact support and Kronecker delta function,use penalty method to apply the essential boundary conditions. In this paper, the RPIM is applied to solving the deformation in one and two dimensional solids by different loads, the results demonstrated that the meshfree RPIM can effectively solve material mechanics problems.

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XU, XU, YUANTONG GU, and GUIRONG LIU. "A HYBRID SMOOTHED FINITE ELEMENT METHOD (H-SFEM) TO SOLID MECHANICS PROBLEMS." International Journal of Computational Methods 10, no. 01 (February 2013): 1340011. http://dx.doi.org/10.1142/s0219876213400112.

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In this paper, a hybrid smoothed finite element method (H-SFEM) is developed for solid mechanics problems by combining techniques of finite element method (FEM) and node-based smoothed finite element method (NS-FEM) using a triangular mesh. A parameter α is equipped into H-SFEM, and the strain field is further assumed to be the weighted average between compatible stains from FEM and smoothed strains from NS-FEM. We prove theoretically that the strain energy obtained from the H-SFEM solution lies in between those from the compatible FEM solution and the NS-FEM solution, which guarantees the convergence of H-SFEM. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper- and lower-bound solutions can always be obtained by adjusting α; (2) there exists a preferable α at which the H-SFEM can produce the ultrasonic accurate solution.

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Givoli, Dan. "Exact Representations on Artificial Interfaces and Applications in Mechanics." Applied Mechanics Reviews 52, no. 11 (November 1, 1999): 333–49. http://dx.doi.org/10.1115/1.3098920.

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In various areas of applied mechanics, there are instances where it is necessary or beneficial to represent the behavior of a mechanical system on an artificial boundary, or artificial interface, which is introduced into the system. Examples include, among others, the computational treatment of mechanical problems in infinite media, the solution of crack problems in fracture mechanics, the dynamical analysis of a mechanical system attached to a number of smaller subsystems, iterative domain decomposition methods, and the mathematical formulation of inverse problems. The representation of the solution on the interface may be approximate or exact. This article is concerned with exact representations. It explains the benefit in using such representations, compares them to approximate representations in various respects, surveys work that has been done in this field, and highlights applications in applied mechanics. It is the author’s opinion that despite the fact that approximate interface representations are more popular than exact ones, the latter have definite advantages in many situations. References cited in this review article number 163.

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Segalman, Daniel J., Michael J. Starr, and Martin W. Heinstein. "New Approximations for Elastic Spheres Under an Oscillating Torsional Couple." Journal of Applied Mechanics 72, no. 5 (December 2, 2004): 705–10. http://dx.doi.org/10.1115/1.1985430.

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The Lubkin solution for two spheres pressed together and then subjected to a monotonically increasing axial couple is examined numerically. The Deresiewicz asymptotic solution is compared to the full solution and its utility is evaluated. Alternative approximations for the Lubkin solution are suggested and compared. One approximation is a Padé rational function which matches the analytic solution over all rotations. The other is an exponential approximation that reproduces the asymptotic values of the analytic solution at infinitesimal and infinite rotations. Finally, finite element solutions for the Lubkin problem are compared with the exact and approximate solutions.

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29

Chandrasekharaiah, D. S. "A complete solution in elastodynamics." Acta Mechanica 84, no. 1-4 (March 1990): 185–90. http://dx.doi.org/10.1007/bf01176096.

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30

Borodachev, N. M. "Thermoelastic Solution for Stresses." International Applied Mechanics 41, no. 3 (March 2005): 264–71. http://dx.doi.org/10.1007/s10778-005-0083-7.

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Felszeghy, S. F. "The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 1: Steady-State Response." Journal of Vibration and Acoustics 118, no. 3 (July 1, 1996): 277–84. http://dx.doi.org/10.1115/1.2888178.

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The response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions are developed in Part 1 of this article for all load speeds greater than zero. It is shown that a steady-state solution which is identically zero ahead of the load front exists at every load speed, in the sense of generalized functions, including the critical speeds when the load travels at the minimum phase velocity of propagating harmonic waves and the sonic speeds. The solution to the homogeneous equations of motion is developed in Part 2 where the two solutions in question are summed and numerical results are presented as well.

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Pitarch, Jes�s, Juan-Luis Pascual-Ahuir, Estanislao Silla, I�aki Tu��n, and Manuel F. Ruiz-L�pez. "Modeling ?-lactam interactions in aqueous solution through combined quantum mechanics-molecular mechanics methods." Journal of Computational Chemistry 20, no. 13 (October 1999): 1401–11. http://dx.doi.org/10.1002/(sici)1096-987x(199910)20:13<1401::aid-jcc7>3.0.co;2-m.

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Ping, Qi, Chen Wang, Qi Gao, Kaifan Shen, Yulin Wu, Shuo Wang, and Xiangyang Li. "Experimental Study on Dynamic Compression Mechanics of Sandstone after Coupled Alkali-Chemical-Dynamic Interaction." Advances in Civil Engineering 2022 (October 10, 2022): 1–10. http://dx.doi.org/10.1155/2022/1970591.

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For the purpose of analyzing the effect of the alkaline solutions on the mechanical property of sandstone impact compression, the sandstone specimens of coal mine roadway were corroded in NaOH solution with pH 7 (neutral pure water solution) and pH = 8, 9, 10, 11, and 12 for 28 d, followed by dynamic compression tests using a separated Hopkinson compression bar test device, and the microstructural changes of the specimens were measured by SEM electron microscope scanning equipment. The studies indicate that the degree of damage to the dynamic properties of a sandstone specimen is tightly correlated with the variation of the pH value of the corrosion solution. The corrosion deterioration effect of the strong alkaline solution is most obvious, followed by the weak alkaline solution, and the mechanical properties of the sandstone are relatively stable under a neutral solution. The dynamic compressive strength and dynamic modulus of elasticity of specimens decrease as a quadratic and cubic function, respectively, with the rising pH of the solution. The dynamic peak strain and average strain rate tend to increase with the increase in pH, and they are larger than those of the uncorroded specimens. As the pH of the solution rises, the impact damage of the sandstone specimens intensifies, and the average particle size of the fragments tends to decrease in a quadratic polynomial.

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34

Goman, O. G. "Solution of the equations of thermoelasticity." Soviet Applied Mechanics 22, no. 6 (June 1986): 544–51. http://dx.doi.org/10.1007/bf00890608.

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Zaytsev, M. L., and V. B. Akkerman. "EXPLICIT TRANSFORMATION OF THE RICCATI EQUATION AND OTHER POLYNOMIAL ODES TO SYSTEMS OF LINEAR ODES." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 72 (2021): 5–14. http://dx.doi.org/10.17223/19988621/72/1.

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The purpose of this work is to propose and demonstrate a way to explicitly transform polynomial ODE systems to linear ODE systems. With the help of an additional first integral, the one-dimensional Riccati equation is transformed to a linear system of three ODEs with variable coefficients. Solving the system, we can find a solution to the original Riccati equation in the general form or only to the Cauchy problem. The Riccati equation is one of the most interesting nonlinear first order differential equations. It is proved that there is no general solution of the Riccati equation in the form of quadratures; however, if at least one particular solution is known, then its general solution is also found. Thus, it is enough only to find a particular solution of the linear system of ODEs. The applied transformation method is a special case of the method described in our work [Zaytsev M. L., Akkerman V. B. (2020) On the identification of solutions to Riccati equation and the other polynomial systems of ODEs // preprint, Research Gate. DOI: 10.13140 / RG.2.2.26980.60807]. This method uses algebraic transformations and transition to new unknowns consisting of products of the original unknowns. The number of new unknowns becomes less than the number of equations. For the multidimensional Riccati equations, we do not present the corresponding linear system of ODEs because of the large number of linear equations obtained (more than 100). However, we present the first integral with which this can be done. In this paper, we also propose a method for finding the first integral, which can be used to reduce a search for the solution of any polynomial systems of ODEs to a search of solutions to linear systems of ODEs. In particular, if the coefficients in these equations are constant, then the solution is found explicitly.

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Han, Weimin. "Numerical analysis of stationary variational-hemivariational inequalities with applications in contact mechanics." Mathematics and Mechanics of Solids 23, no. 3 (June 27, 2017): 279–93. http://dx.doi.org/10.1177/1081286517713342.

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This paper is devoted to numerical analysis of general finite element approximations to stationary variational-hemivariational inequalities with or without constraints. The focus is on convergence under minimal solution regularity and error estimation under suitable solution regularity assumptions that cover both internal and external approximations of the stationary variational-hemivariational inequalities. A framework is developed for general variational-hemivariational inequalities, including a convergence result and a Céa type inequality. It is illustrated how to derive optimal order error estimates for linear finite element solutions of sample problems from contact mechanics.

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Zhang, Wx. "Basic Solutions of Three Dimensional Elasticity." E3S Web of Conferences 236 (2021): 05039. http://dx.doi.org/10.1051/e3sconf/202123605039.

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Elastic calculation method is an important research content of computational mechanics. The problems of elasticity include basic equations and boundary conditions. Therefore, the final solution consists of the general solutions of the basic equations and the special solutions satisfying the boundary conditions. Numerical method is often used in practical calculation, but the analytical solution is also an important subject for researchers. In this paper, the basic solution of three-dimensional elastic materials is given by theoretical derivation.

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M, Nivetha, Sujtha S, and Abinaya V. "Vehicle Breakdown Assistance." International Journal on Cybernetics & Informatics 10, no. 2 (May 31, 2021): 193–202. http://dx.doi.org/10.5121/ijci.2021.100221.

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This application is used to find nearby area mechanics while we suddenly stranded on the remote locations with mechanical issues of our vehicle. It is a good solution for the people who seek help in the remote locations. In this, the approved mechanics are enlisted in this application. Also they are under monitored by this system for not charging any extra service fee from the users. This can be monitored by the admin through the user feedback based on their service. The registered users can access this application. This application will help to reduce wasting user time to found a proper mechanic. This application will allow user to make payment for a vehicle repair in a reasonable price.

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Felszeghy, S. F. "The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 2: Transient Response." Journal of Vibration and Acoustics 118, no. 3 (July 1, 1996): 285–91. http://dx.doi.org/10.1115/1.2888179.

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The transient response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions were developed in Part 1 of this article for all load speeds greater than zero. The solution to the homogeneous equations of motion is developed here in Part 2. It is shown that the latter solution can be obtained by numerical integration using the method of characteristics. Particular attention is given to the cases when the load travels at the critical speeds consisting of the minimum phase velocity of propagating harmonic waves and the sonic speeds. It is shown that the solution to the homogeneous equations combines with the steady-state solution in such a manner that the beam displacements are continuous and bounded for all finite times at all load speeds including the critical speeds. Numerical results are presented for the critical load speed cases.

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Guo, Jin Jun, Ju Hong Han, and Zhe Ting Xu. "Experimental Study on Mechanics Behavior of Modified Concrete Subjected to Composite Corrosion Solution." Advanced Materials Research 374-377 (October 2011): 1485–90. http://dx.doi.org/10.4028/www.scientific.net/amr.374-377.1485.

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For revealing the behaviors of modified concrete materials against eroding from composite solution, accelerated deterioration tests of Portland concrete, polypropylene fiber concrete, fly ash concrete and concrete mixed with polypropylene fiber and fly ash were made under continuous immersion in two types of composite corrosion solutions, which were sulfate composite solution and magnesium composite solution. The compressive strength, splitting tensile strength and elastic modulus of modified concrete subjected to corrosion were detected. The results show that capacity of corrosion resistance of concrete is enhanced remarkably by modifying approach of mixing fly ash and polypropylene fiber into concrete. The deteriorated splitting tensile strength of modified concrete is able to be increased by 30%-60% compared with ordinary concrete. The research results are benefit to engineering design and application.

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Stąpór, Paweł. "An Improved XFEM for the Poisson Equation with Discontinuous Coefficients." Archive of Mechanical Engineering 64, no. 1 (March 1, 2017): 123–44. http://dx.doi.org/10.1515/meceng-2017-0008.

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Abstract Discontinuous coefficients in the Poisson equation lead to the weak discontinuity in the solution, e.g. the gradient in the field quantity exhibits a rapid change across an interface. In the real world, discontinuities are frequently found (cracks, material interfaces, voids, phase-change phenomena) and their mathematical model can be represented by Poisson type equation. In this study, the extended finite element method (XFEM) is used to solve the formulated discontinuous problem. The XFEM solution introduce the discontinuity through nodal enrichment function, and controls it by additional degrees of freedom. This allows one to make the finite element mesh independent of discontinuity location. The quality of the solution depends mainly on the assumed enrichment basis functions. In the paper, a new set of enrichments are proposed in the solution of the Poisson equation with discontinuous coefficients. The global and local error estimates are used in order to assess the quality of the solution. The stability of the solution is investigated using the condition number of the stiffness matrix. The solutions obtained with standard and new enrichment functions are compared and discussed.

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Wang, Jialai, and Pizhong Qiao. "Mechanics of Bimaterial Interface: Shear Deformable Split Bilayer Beam Theory and Fracture." Journal of Applied Mechanics 72, no. 5 (February 2, 2005): 674–82. http://dx.doi.org/10.1115/1.1978920.

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A novel split beam model is introduced to account for the local effects at the crack tip of bi-material interface by modeling a bi-layer composite beam as two separate shear deformable beams bonded perfectly along their interface. In comparisons with analytical two-dimensional continuum solutions and finite element analysis, better agreements are achieved for the present model, which is capable of capturing the local deformation at the crack tip in contrast to the conventional composite beam theory. New solutions of two important issues of cracked beams, i.e., local buckling and interface fracture, are then presented based on the proposed split bi-layer shear deformable beam model. Local buckling load of a delaminated beam considering the root rotation at the delamination tip is first obtained. By considering the root rotation at the crack tip, the buckling load is lower than the existing solution neglecting the local deformation at the delamination tip. New expressions of energy release rate and stress intensity factor considering the transverse shear effect are obtained by the solution of local deformation based on the novel split beam model, of which several new terms associated with the transverse shear force are present, and they represent an improved solution compared to the one from the classical beam model. Two specimens are analyzed with the present model, and the corresponding refined fracture parameters are provided, which are in better agreement with finite element analysis compared to the available classical solutions.

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Wang, Dunyou, Marat Valiev, and Bruce C. Garrett. "CH2Cl2+ OH−Reaction in Aqueous Solution: A Combined Quantum Mechanical and Molecular Mechanics Study." Journal of Physical Chemistry A 115, no. 8 (March 3, 2011): 1380–84. http://dx.doi.org/10.1021/jp109287r.

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Lai, C. Y., K. R. Rajagopal, and A. Z. Szeri. "Asymmetric flow above a rotating disk." Journal of Fluid Mechanics 157 (August 1985): 471–92. http://dx.doi.org/10.1017/s0022112085002452.

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In this paper we generalize the von Kármán solution for flow above a single rotating disk, to include non-axisymmetric solutions. These solutions contain an arbitrary parameter; for zero value of the parameter the asymmetric flow degenerates into the classical von Kármán solution. Thus the classical solution is never isolated when considered within the scope of the full Navier–Stokes equations; there are asymmetric solutions in every neighbourhood of the von Kármán solution. Calculations are reported here for s = 0, 0.02 and 0.06, where s represents the ratio of angular velocity of the fluid at infinity to the angular velocity of the disk. A subset of the solutions obtained here corresponds to flow induced by the rotation of a disk when the latter is placed in a fluid that is moving with a constant uniform velocity.

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Sanderson, Brian. "A Lagrangian solution for internal waves." Journal of Fluid Mechanics 152 (March 1985): 191–202. http://dx.doi.org/10.1017/s0022112085000647.

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A perturbation procedure is used to obtain first- and second-order solutions for small-amplitude internal waves in a Lagrangian coordinate system. The first-order Lagrangian equations are formally accurate to the same order as the first-order Eulerian equations; however, they are different and the Lagrangian solution gives a more realistic wave shape. First-order Lagrangian solutions for internal waves in uniformly stratified fluid have a shape similar to that found in the second-order Eulerian solution. Wave profiles in uniformly stratified fluid exhibit broad crests and narrow troughs near the surface, a sinusoidal shape at mid-depth, and narrow crests and broad troughs near the bottom. The difference between the shape of crests and troughs grows as the wave amplitude is increased. Solutions obtained in a uniformly stratified fluid with a small bottom slope yield plausible shapes for breaking waves.

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46

Carroll, M. M. "Foundations of Solid Mechanics." Applied Mechanics Reviews 38, no. 10 (October 1, 1985): 1301–8. http://dx.doi.org/10.1115/1.3143698.

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Solid mechanics is a basic discipline which supports much of the practice of mechanical and civil engineering, and contributes significantly to other engineering and scientific disciplines. Research in solid mechanics, at the foundational level, emphasizes comprehensive understanding and well-formulated analyses of mechanical phenomena occurring in engineering systems. The increasing availability of large computers has had a tremendous impact on the field. The traditional emphasis on analysis has shifted toward development of more realistic and detailed descriptions of material response, more efficient computational methodologies, and accurate numerical solution of initial and boundary value problems. Despite (or perhaps because of) this trend, theory and analysis must continue to play a vital role in modern solid mechanics. Solid mechanics is enriched by the increasing level of activity in interdisciplinary research. Within the field, there is a need for better communication and interaction between computation, experiment, and theory.

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Aulova, Alexandra, Marko Bek, Leonid Kossovich, and Igor Emri. "Needleless Electrospinning of PA6 Fibers: The Effect of Solution Concentration and Electrospinning Voltage on Fiber Diameter." Strojniški vestnik – Journal of Mechanical Engineering 66, no. 7-8 (July 15, 2020): 421–30. http://dx.doi.org/10.5545/sv-jme.2020.6713.

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Needleless electrospinning is the process of forming thin material fibers from the open surface of its solution or melt in a strong electrostatic field. Electrospun non-woven materials are used in various applications that require specific fiber diameters and pore size distributions. Fiber diameter depends on the properties of the polymer solution and manufacturing conditions. A needleless electrospinning process using the Nanospider setup was investigated using the commonly used polyamide 6 (PA6) solution in a mixture of acetic and formic acids. Polymer solutions with different polymer concentrations were characterized by viscosity, surface tension and electrical conductivity. An increase in polymer content in the solution resulted in the exponential increase of the solution viscosity, polynomial increase of electrical conductivity and had almost no effect on surface tension. The effect of the polymer concentration in the solution, as well as electrospinning voltage on fiber diameter and diameter distribution, was investigated using scanning electron microscopy images. The average fiber diameter linearly increases with the increased polymer concentration and also demonstrates an increase with increased electrospinning voltage, although less pronounced. Therefore, a change in the PA6 solution concentration should be used for the robust adjustment of fiber diameter, while changes in electrospinning voltage are more appropriate for fine tuning the fiber diameter during the process of needleless electrospinning.

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Chandrasekharaiah, D. S. "Naghdi-Hsu type solution in elastodynamics." Acta Mechanica 76, no. 3-4 (March 1989): 235–41. http://dx.doi.org/10.1007/bf01253582.

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Bouyarmane, Houda, Amine El, and Mohammed Sallaou. "Early environmental assessment of products using behavior models and the impact of their inaccuracy on environmental product performance." FME Transactions 50, no. 4 (2022): 715–23. http://dx.doi.org/10.5937/fme2204715b.

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The decisions made during the preliminary design phases considerably impact the development of a product's lifecycle, acting on its environmental performance, cost, and duration of its realization. However, the lack of relevant information during these phases does not allow for the accurate evaluation of design solutions. In addition, it generates schedule delays and overruns in the budget allocated to developing a given solution. In this perspective, the present work aims to assess the accuracy of the behavior models used for exploring solutions during the embodiment phase. This was based on two measures of different nature, namely objective accuracy, which is evaluated by referring to real prototyping of a given solution, and the subjective accuracy measure, which allows to the expression of the degradation of the first measure in relation to the reference point. This combination will lead to a measure that can be generalized on all the design space. In a second step, the current work suggests an estimation of the effect of these models' accuracy on the proposed solutions' environmental impact. To this end, a sensitivity study was carried out on the input data of the model (design parameters) in order to deduce the effect of the results obtained (performance parameters) on the mass and, consequently, the environmental impact of the solution. In order to highlight the approach adopted in the present study, it was applied to a real industrial case, ultimately leading to the most optimized solution in terms of accuracy and environmental impact.

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Mau, S. T. "Elastica Solution of Braced Struts." Journal of Engineering Mechanics 116, no. 3 (March 1990): 688–97. http://dx.doi.org/10.1061/(asce)0733-9399(1990)116:3(688).

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Journal articles on the topic 'Mechanics solution'

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