Simplification through regression analysis on the dynamic response of plates with arbitrary boundary conditions excited by moving inertia load

Dynamic response of a thin rectangular plate traversed by a moving inertia load with arbitrary boundary condition is investigated through this paper. The inertia effect of mass is considered and relevant formulation is established based on the full-term of acceleration, employing the method of Boundary Characteristic Orthogonal Polynomials, BCOP. To acquire the complete solution of partial differential equations governing on the plate, the Galerkin method is used to separate the temporal function from the spatial one. The problem is formulated in the state space and applying the numerical method of Matrix Exponential the complete solution would be achieved. In the numerical studies, a comprehensive parametric study is performed for both cases of loading when inertia effect is included or neglected. Several mass and aspect ratios for the plate with major types of boundary conditions CCCC, SSSS, CFCF and SFSF are accounted for presenting the results. Dynamic amplification factor against velocity parameter is scrutinized within many graphs alongside with a time history analysis of dynamic deflection for the plate's mid-span. Investigating on the dynamic response concludes to the critical boundary condition upon moving mass. By introducing a conversion factor, the margin of inertia and the critical velocity where happened would be achieved, then through a regression analysis a curve fitting model of polynomials is proposed. Corresponding coefficients testify the goodness of fit for such regression which are reported within tables. Referring to this simplified model of conversion factor pertaining to the specific boundary condition, it would be possible to handle the problem in moving load case without undertaking the complexities arisen from inertia contribution into the formulation. Having derived the factor from simplified model which has been calculated for a specific mass and velocity ratio, then multiplying into the moving load response, the complete solution for moving mass would be achieved.     

Investigation of critical influential speed for moving mass problems on beams

A traveling mass due to its mass inertia has significant effects on the dynamic response of the structures. According to recent developments in structural materials and constructional technologies, the structures are likely to be affected by sudden changes of masses and substructure elements, in which the inertia effect of a moving mass is not negligible. The transverse inertia effects have been a topic of interest in bridge dynamics, design of railway tracks, guide way systems and other engineering applications such as modern high-speed precision machinery process. In this study an analytical–numerical method is presented which can be used to determine the dynamic response of beams carrying a moving mass, with various boundary conditions. It has been shown that the Coriolis acceleration, associated with the moving mass as it traverses along the vibrating beam shall be considered as well. Influences regarding the speed of the moving mass on the dynamic response of beams with various boundary conditions were also investigated. Results illustrated that the speed of a moving mass has direct influence on the entire structural dynamic response, depending on its boundary conditions. Critical influential speeds in the moving mass problems were introduced and obtained in numerical examples for various BC’s.     

An incentivized early remediation program in Calculus I

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea that a lack of prerequisite knowledge is a significant hurdle for students, but also that participation in the remediation program is correlated with student success. In addition, the program allows for the very early identification of students at high risk of failing. The program is easy to implement, and it would be adaptable to a variety of other courses for which prerequisite knowledge is essential for success including science courses, engineering courses and other mathematics courses.     

水下爆炸气泡与复杂弹塑性结构的相互作用研究

计及结构的弹塑性,将边界元法(BEM)与有限元法(FEM)耦合提出了气泡与弹塑性结构耦合动力学计算方法,并开发了全套的三维水下气泡分析程序（UBA）,计算值与实验值之间误差在10%以内．以水面舰船为例,将三维计算程序工程化．并分析了水下爆炸气泡载荷作用下船体的弹塑性响应,从船体结构典型单元上的应力时历曲线可以看出,在气泡坍塌时出现应力峰值,证实了气泡坍塌压力及射流引起的压力对舰船等结构造成严重毁伤．从气泡与舰船的相互作用中可以看出,舰船低阶垂向振型被激起,在气泡作用下呈鞭状运动,同时舰船随着气泡的膨胀和收缩作升沉运动,通过本文的分析得到了适合于工程应用的规律及结论．     

拓扑优化技术在抑制流体晃荡中的数值模拟研究

流体晃荡问题广泛存在于船舶与海洋工程领域,任何部分载液的储罐运载装备在运动过程中均存在晃荡问题.当外界激励频率接近液舱内流体自由液面的固有频率时,很容易产生剧烈的晃荡,产生极大的冲击力,进而引起结构损害.因此,研究有效的减晃方案,以抑制流体晃荡带来的冲击具有重要意义.该文研究了基于自主研制的数值程序模拟长方体液舱内的流...     

Application of lower bound direct method to engineering structures

Direct methods provide elegant and efficient approaches for the prediction of the long-term behaviour of engineering structures under arbitrary complex loading independent of the number of loading cycles. The lower bound direct method leads to a constrained non-linear convex problem in conjunction with finite element methods, which necessitates a very large number of optimization variables and a large amount of computer memory. To solve this large-scale optimization problem, we first reformulate it in a simpler equivalent convex program with easily exploitable sparsity structure. The interior point with DC regularization algorithm (IPDCA) using quasi definite matrix techniques is then used for its solution. The numerical results obtained by this algorithm will be compared with those obtained by general standard code Lancelot. They show the robustness, the efficiency of IPDCA and in particular its great superiority with respect to Lancelot.     

A numerical study on statistical temporal scales in inertia particle dispersion

The statistical temporal scales involved in inertia particle dispersion are analyzed numerically. The numerical method of large eddy simulation, solving a filtered Navier-Stokes equation, is utilized to calculate fully developed turbulent channel flows with Reynolds numbers of 180 and 640, and the particle Lagrangian trajectory method is employed to track inertia particles released into the flow fields. The Lagrangian and Eulerian temporal scales are obtained statistically for fluid tracer particles and three different inertia particles with Stokes numbers of 1, 10 and 100. The Eulerian temporal scales, decreasing with the velocity of advection from the wall to the channel central plane, are smaller than the Lagrangian ones. The Lagrangian temporal scales of inertia particles increase with the particle Stokes number. The Lagrangian temporal scales of the fluid phase ‘seen’ by inertia particles are separate from those of the fluid phase, where inertia particles travel in turbulent vortices, due to the particle inertia and particle trajectory crossing effects. The effects of the Reynolds number on the integral temporal scales are also discussed. The results are worthy of use in examining and developing engineering prediction models of particle dispersion.     

Computers and the Civil Engineer

The tasks engaged upon by a civil or structural engineer when designing a road or multistorey structure would appear to be ideal for digital computers. Some of the reasons why engineers do not use computers more heavily are examined and the fundamental difficulty due to the variable nature of the work is outlined. Some successful applications in structural and highway engineering are described where the calculation steps are sufficiently well ordered for a standard computer program to be successful. A new development, that of problem‐oriented language is described showing the advantages such systems have over conventional programs. Reference is made to GENESYS, a General Engineering System now being developed for the Ministry of Public Building and Works of the United Kingdom, which allows problem‐oriented languages to be devised for use in application.     

A GENERATOR AND A SIMPLEX SOLVER FOR NETWORK PIECEWISE LINEAR PROGRAMS

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Solving fractional problems with dynamic multistart improving hit-and-run

Fractional programming has numerous applications in economy and engineering. While some fractional problems are easy in the sense that they are equivalent to an ordinary linear program, other problems like maximizing a sum or product of several ratios are known to be hard, as these functions are highly nonconvex and multimodal. In contrast to the standard Branch-and-Bound type algorithms proposed for specific types of fractional problems, we treat general fractional problems with stochastic algorithms developed for multimodal global optimization. Specifically, we propose Improving Hit-and-Run with restarts, based on a theoretical analysis of Multistart Pure Adaptive Search (cf. the dissertation of Khompatraporn (2004)) which prescribes a way to utilize problem specific information to sample until a certain level α of confidence is achieved. For this purpose, we analyze the Lipschitz properties of fractional functions, and then utilize a unified method to solve general fractional problems. The paper ends with a report on numerical experiments. This work was initiated while Mirjam Dür was spending a three-month research visit at the University of Washington. She would like to thank the Fulbright Commission for financial support and the optimization group at UW for their warm hospitality. The work of C. Khompatraporn and Z.B. Zabinsky was partially supported by the NSF grant DMI-0244286.     

Engineering process as a focus: STEM professional development with elementary STEM‐focused professional development schools

Young children are capable of engaging in STEM investigations when they are guided by skilled and knowledgeable teachers. However, many elementary teachers may lack sufficient STEM content knowledge and report feeling unprepared to teach STEM content. Two university faculty members in mathematics and science education, worked to cultivate and advance two designated Elementary STEM‐Focused professional development schools through a two year series of an after‐school STEM professional development (PD) Program. As the STEM PD Program progressed, it became evident that teachers were interested in and needed more experiences with the elements of the engineering process for young learners. With this in mind, several of the PD sessions were designed to highlight the engineering process and allow teachers to experience various activities that would engage young learners. To examine how this focus on the engineering process impacted the teachers in this STEM PD Program, a research study was organized during year two of the STEM PD Program. The results of this study provide evidence that this program had a positive influence on the teacher participants’ engineering teacher efficacy and implementation of engineering lessons and activities within their classrooms.     

The projection method of optimization applied to engineering plasticity problems

In engineering plasticity, the behavior of a structure (e.g., a frame or truss) under a variety of loading conditions is studied. Two primary types of analysis are generally conducted. Limit analysis determines the rigid plastic collapse load for a structure and can be formulated as a linear program (LP). Deformation analysis at plastic collapse can be formulated as a quadratic program (QP). The constraints of the two optimization problems are closely related. This paper presents a specialization of the projection method for linear programming for the limit-load analysis problem. The algorithm takes advantage of the relationship between the LP constraints and QP constraints to provide advantageous starting data for the projection method applied to the QP problem. An important feature of the method is that it avoids problems of apparent infeasibility due to roundoff errors. Experimental results are given for two medium-sized problems.This work was supported by the National Research Council of Canada under Research Grant No. A8189.     

Inertia effects in circular squeeze film bearing using Herschel–Bulkley lubricants

Recent engineering trends in lubrication emphasize that in order to analyze the performance of bearings adequately, it is necessary to take into account the combined effects of fluid inertia forces and non-Newtonian characteristics of lubricants. In the present work, the effects of fluid inertia forces in the circular squeeze film bearing lubricated with Herschel–Bulkley fluids with constant squeeze motion have been investigated. Herschel–Bulkley fluids are characterized by an yield value which leads to the formation of a rigid core in the flow region. The shape and extent of the core formation along the radial direction is determined numerically for various values of Herschel–Bulkley number and power-law index. The bearing performances such as pressure distribution and load capacity for different values of Herschel–Bulkley number, Reynolds number, power-law index have been computed. The effects of fluid inertia and non-Newtonian characteristics on the bearing performances have been discussed.     

Exact penalty results for mathematical programs with vanishing constraints

A mathematical program with vanishing constraints (MPVC) is a constrained optimization problem arising in certain engineering applications. The feasible set has a complicated structure so that the most familiar constraint qualifications are usually violated. This, in turn, implies that standard penalty functions are typically non-exact for MPVCs. We therefore develop a new MPVC-tailored penalty function which is shown to be exact under reasonable assumptions. This new penalty function can then be used to derive (or recover) suitable optimality conditions for MPVCs.     

Eigenvalue Multiplicity Estimate in Semidefinite Programming

A semidefinite programming problem is a mathematical program in which the objective function is linear in the unknowns and the constraint set is defined by a linear matrix inequality. This problem is nonlinear, nondifferentiable, but convex. It covers several standard problems (such as linear and quadratic programming) and has many applications in engineering. Typically, the optimal eigenvalue multiplicity associated with a linear matrix inequality is larger than one. Algorithms based on prior knowledge of the optimal eigenvalue multiplicity for solving the underlying problem have been shown to be efficient. In this paper, we propose a scheme to estimate the optimal eigenvalue multiplicity from points close to the solution. With some mild assumptions, it is shown that there exists an open neighborhood around the minimizer so that our scheme applied to any point in the neighborhood will always give the correct optimal eigenvalue multiplicity. We then show how to incorporate this result into a generalization of an existing local method for solving the semidefinite programming problem. Finally, a numerical example is included to illustrate the results.     

关于任意边界缺口或裂纹群问题的一类解法(Ⅰ)解析方法

在工程断裂分析中任意边界缺陷如缺口或裂纹群是常见和重要的情况.本文推广穆斯赫利施维利方法作出了任意二维边界缺口或裂纹群问题的一类解法,通过相继应用解析延拓、劳朗级数展开和共形映照.我们最终获得支配问题的一组线性代数方程,然后应用标准的线代数方程组求解程序对问题就作出了解答.值得注意的是.本文方法可用于作出缺陷表面具有任意的光滑载荷分布情况的解答.     

Portfolio selection under downside risk measures and cardinality constraints based on DC programming and DCA

In this paper, we consider the case of downside risk measures with cardinality and bounding constraints in portfolio selection. These constraints limit the amount of capital to be invested in each asset as well as the number of assets composing the portfolio. While the standard Markowitz’s model is a convex quadratic program, this new model is a NP-hard mixed integer quadratic program. Realizing the computational intractability for this class of problems, especially large-scale problems, we first reformulate it as a DC program with the help of exact penalty techniques in Difference of Convex functions (DC) programming and then solve it by DC Algorithms (DCA). To check globality of computed solutions, a global method combining the local algorithm DCA with a Branch-and-Bound algorithm is investigated. Numerical simulations show that DCA is an efficient and promising approach for the considered problem.      

Application of sequential quadratic programming software program to an actual problem

We produced a nonlinear optimization software program which is based on a Sequential Quadratic Programming (SQP) method (Schittkowski, 1981a). Our program has several original characteristics: (1) automatic choice between two QP solvers, the Goldfarb—Idnani (GI) method (Goldfarb and Idnani, 1983) and the Least Squares (LS) method (Schittkowski, 1981b); (2) an augmented Lagrange function (Schittkowski, 1981a) as the objective function for line search; (3) adaptive Armijo method for line search; (4) direct definition of upper and lower bounds for variables and constraint functions; and (5) accurate numerical differentials. These characteristics ensure the reliability of our program for solving standard problems. In this paper, point (3) is described in detail. Then, the program is applied to an actual problem, the optimal placement of blocks. A model for this problem has been suggested by Sha and Dutton (1984), but it was unsuited to treatment by the SQP method. Thus we modify it to ensure program applicability.     

非线性互补约束规划问题的一个新的QP-free算法

本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.     

Nonlinearly coupled in-plane and transverse vibrations of a spinning disk

Previous nonlinear spinning disk models neglected the in-plane inertia of the disk since this permits the use of a stress function. This paper aims to consider the effect of including the in-plane inertia of the disk on the resulting nonlinear dynamics and to construct approximate solutions that capture the new dynamics. The inclusion of the in-plane inertia results in a nonlinear coupling between the in-plane and transverse vibrations of the spinning disk. The full nonlinear partial differential equations are simplified to a simpler nonlinear two degrees of freedom model via the method of Galerkin. A canonical perturbation approach is used to derive an approximate solution to this simpler nonlinear problem. Numerical simulations are used to evaluate the effectiveness of the approximate solution. Through the use of these analytical and numerical tools, it becomes apparent that the inclusion of in-plane inertia gives rise to new phenomena such as internal resonance and the possibility of instability in the system that are not predicted if the in-plane inertia is ignored. It is also demonstrated that the canonical perturbation approach can be used to produce an effective approximate solution.