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The authors search the optimal distribution of bending flexure along the axis of the rod. For the solution of the actual problem, the stability equations take into account all possible convex, simply connected shapes of the cross-section. The authors study the cross-sections with equal principal moments of inertia. The cross-sections are similar geometric figures related by a homothetic transformation with respect to a homothetic center on the axis of the rod and vary along its axis. The cross-section that delivers the maximum or the minimum for the critical eigenvalue must be determined among all convex, simply connected domains. The optimal form of the cross-section is known to be an equilateral triangle. The distribution of material along the length of a twisted and compressed rod is optimized so that the rod must support the maximal moment without spatial buckling, presuming its volume remains constant among all admissible rods. The static Euler's approach is applicable for simply supported rod (hinged), twisted by the conservative moment and axial compressing force.

The optimization problems for stability of twisted and compressed rods are studied in this manuscript. The complement for Euler's buckling problem is Greenhill's problem, which studies the forming of a loop in an elastic bar under simultaneous torsion and compression (Greenhill, 1883).

For determining the optimal solution, the authors directly compare the twisted rods with the different lengths and cross-sections using the invariant factors. The solution of optimization problem for simultaneously twisted and compressed rod is stated in closed form.

(1) The linear stability equations are applied. (2) No nonlinear or postbuckling effects were accounted. (3) The moment-free, ideal boundary conditions on both ends of the rod assumed.

One of the most common design cases in mechanical engineering is the concurrent compression and twisting of the straight members. The closed-form solution allows the immediate estimation of the optimization effect for axes and rotors in industrial and automotive engineering.

The application of lighter and material-saving structural elements allow the saving fabrication resources, reducing the mass of vehicles and industry machines. The systematic usage of material optimized structural elements assists the stabilization of global energy balance of Earth.

Albeit the governing ordinary differential equations are linear, the application of the optimality conditions leads to the nonlinearity of the final optimization equations. The search of closed form solution of the nonlinear differential equations is one of the mathematically hardest tasks in engineering mathematics. The closed-form solution presents in terms of higher transcendental functions.

The purpose of this paper is to develop the method for the calculation of residual stress and enduring deformation of helical springs.

For helical compression or tension springs, a spring wire is twisted. In the first case, the torsion of the straight bar with the circular cross-section is investigated, and, for derivations, the StVenant’s hypothesis is presumed. Analogously, for the torsion helical springs, the wire is in the state of flexure. In the second case, the bending of the straight bar with the rectangular cross-section is studied and the method is based on Bernoulli’s hypothesis.

For both cases (compression/tension of torsion helical spring), the closed-form solutions are based on the hyperbolic and on the Ramberg–Osgood material laws.

The method is based on the deformational formulation of plasticity theory and common kinematic hypotheses.

The advantage of the discovered closed-form solutions is their applicability for the calculation of spring length or spring twist angle loss and residual stresses on the wire after the pre-setting process without the necessity of complicated finite-element solutions.

The formulas are intended for practical evaluation of necessary parameters for optimal pre-setting processes of compression and torsion helical springs.

Because of the discovery of closed-form solutions and analytical formulas for the pre-setting process, the numerical analysis is not necessary. The analytical solution facilitates the proper evaluation of the plastic flow in torsion, compression and bending springs and improves the manufacturing of industrial components.

In this addendum, the purpose of this paper is to introduce the new creep law for the description of the different stages of creep. The introduced creep law generalizes the creep law used in Kobelev (2014).

The new generalized creep law demonstrates the relationship between creep rate and stress as well as accounts the time dependence in different creep regimes. In the stage of primary creep there is explicit time dependence of creep rate. In the stage of secondary creep the creep rate exhibits – analogously to the original creep law – no explicit dependence on time.

The closed form expressions giving the torque and bending moment as a function of the time are provided. The method is applicable for definite other stress functions in the creep law.

The arbitrary creep law allows the separation of time and spatial variables; exponential and power-law time dependence.

The results of creep simulation are applied to practically important problem of engineering, namely for simulation of creep and relaxation of helical and disk spring, driveshafts, torque elements of machine dynamics.

The new creep model with fractional derivative of time dependence is introduced. The closed form solutions for new creep model allow simple formulas for creep effect on stress and deformation and the implications for high temperature design.

Under this heading are published regularly abstracts of all Reports and Memoranda of the Aeronautical Research Committee, Reports and Technical Notes of the U.S. National Advisory Committee for Aeronautics, and publications of other similar research bodies as issued

IN 1937, when Imperial Airways and Pan American were conducting their flight surveys of the North Atlantic route with developed Empire boats and Sikorsky 42's respectively, and later, in 1939, when Pan American had just opened up their first scheduled Transatlantic Service with Boeing 314's, the design staff of Saunders‐Roe were engaged on the study of a flying‐boat to meet the same requirements.

The purpose of this paper is to describe the implementation of discrete singular convolution (DSC) method to steady seepage flow while presenting one of the possible uses of DSC method in geotechnical engineering. It also aims to present the implementation of DSC to the problems with mixed boundary conditions.

Second order spatial derivatives of potential and stream functions in Laplace's equation are discretized using the DSC method in which the regularized Shannon's delta kernel is used as an approximation to delta distribution. After implementation of boundary conditions, the system of equations is solved for the unknown terms.

The results are compared with those obtained from the finite element method and the finite difference method.

The method is applied to the flow problem through porous medium for the first time.

The purpose of this study is to simultaneously determine the constitutive parameters and boundary conditions by solving inverse mechanical problems of power hardening elastoplastic materials in three-dimensional geometries.

The power hardening elastoplastic problem is solved by the complex variable finite element method in software ABAQUS, based on a three-dimensional complex stress element using user-defined element subroutine. The complex-variable-differentiation method is introduced and used to accurately calculate the sensitivity coefficients in the multiple parameters identification method, and the Levenberg–Marquardt algorithm is applied to carry out the inversion.

Numerical results indicate that the complex variable finite element method has good performance for solving elastoplastic problems of three-dimensional geometries. The inversion method is effective and accurate for simultaneously identifying multi-parameters of power hardening elastoplastic problems in three-dimensional geometries, which could be employed for solving inverse elastoplastic problems in engineering applications.

The constitutive parameters and boundary conditions are simultaneously identified for power hardening elastoplastic problems in three-dimensional geometries, which is much challenging in practical applications. The numerical results show that the inversion method has high accuracy, good stability, and fast convergence speed.

How to get a lighter and stronger anti-rolling torsion bar has become a barrier for the development of high-speed railway vehicles. The purpose of this paper is to realize the multi-objective optimization of an anti-rolling torsion bar with a Modified Non-dominated Sorting Genetic Algorithm III (MNSGA-III), which aims to obtain a better design scheme of an anti-rolling torsion bar device.

First, the Non-dominated Sorting Genetic Algorithm III (NSGA-III) uses a simulated binary crossover (SBX) operator and a polynomial mutation operator, while the MNSGA-III algorithm proposed in this paper introduces an arithmetic crossover and an adaptive mutation operator to change the crossover and mutate operator in NSGA-III. Second, two algorithms are tested by ZDT3, ZDT4 functions. Both algorithms set the same population size and evolutionary generation, and then compare the results of NSGA-III and MNSGA-III. Finally, MNSGA-III is applied to the multi-objective model of an anti-rolling torsion bar which is established by taking the mass and stiffness of the torsion bar as the optimization object. After that, it obtains the Pareto solution set by solving the multi-objective model with MNSGA-III. The only optimal solution selected from the Pareto solution set is compared with the traditional design scheme of an anti-rolling torsion bar.

The MNSGA-III converges faster than NSGA-III. Besides, MNSGA-III has better diversity of Pareto solutions than NSGA-III and is closer to the ideal Pareto frontier. Comparing with the results before the optimization, it shows that the volume of the anti-rolling torsion bar reduces by 1.6 percent and the stiffness increases by 3.3 percent. The optimized data verifies the effectiveness of this method proposed in this paper.

The simulated binary crossover operator and polynomial mutation operator of NSGA-III are changed into an arithmetic crossover operator and an adaptive mutation operator, respectively, which improves the optimization performance of the algorithm.

This study aims to reduce the redundant weight of the anti-roll torsion bar brought by the traditional empirical design and improving its strength and stiffness.

Based on the finite element approach coupled with the improved beluga whale optimization (IBWO) algorithm, a collaborative optimization method is suggested to optimize the design of the anti-roll torsion bar structure and weight. The dimensions and material properties of the torsion bar were defined as random variables, and the torsion bar's mass and strength were investigated using finite elements. Then, chaotic mapping and differential evolution (DE) operators are introduced to improve the beluga whale optimization (BWO) algorithm and run case studies.

The findings demonstrate that the IBWO has superior solution set distribution uniformity, convergence speed, solution correctness and stability than the BWO. The IBWO algorithm is used to optimize the anti-roll torsion bar design. The error between the optimization and finite element simulation results was less than 1%. The weight of the optimized anti-roll torsion bar was lessened by 4%, the maximum stress was reduced by 35% and the stiffness was increased by 1.9%.

The study provides a methodological reference for the simulation optimization process of the lateral anti-roll torsion bar.

The current industry standard rigid spinal implants suffer fatigue failures due to bending and torsion loads. The purpose of this program was to design novel prototype flexible titanium alloy spinal implant rod with machined features, and then apply the laser shock peening (LSP) process to restore the fatigue strength debit due to these features.

A flexible prototype rod was designed with flat section at the center of the rod. The flat section was laser shock peened. Static compression tests were conducted as per American Society of Testing Materials standards for three‐ and four‐point bending tests and “vertebrectomy” constructs. Finite element models were developed to aid in the design of LSP and also to guide the experiments.

The test results indicated a ∼3X improvement in flexibility and a reduction in fatigue load ratio, defined as applied load divided by the yield load; from 72 to 68 percent. This rod was LSP's on the flat sections, and tested again. The results indicated an increase in the fatigue load ratio from 68 to 75 percent without any further change in flexibility.

It has been demonstrated successfully that the current industry rigid spinal implant rod can be modified for flexibility and laser shock peened to increase fatigue strength. This enhancement will enable the use of the implant for longer periods and higher loads; and for surgical processes with and without fusion. This technology can be readily applied to all metals that are certified for human implant applications; thus can be implemented with minimal clinical trials.