Displacement Constraints Research Articles

FEM Simulation Based Computation of Natural Frequencies and Mode Shapes of Loose Transmission Gearbox Casing

The main objective of this research work is to compute the dynamic response in terms of natural frequencies and mode shapes of the heavy vehicle truck transmission gearbox casing subjected to connecting bolts loosening condition. The results of loose transmission casing analysis were compared with the zero displacement constraint condition when casing is tightly mounted on chassis frame using 37 connecting bolts. The loosened transmission causes heavy vibration and noise problem and leads failure of vehicle transmission system. The torsional vibration produces rattling and clattering noise. Reciprocity Principle has been used to determine the frequencies and mode shape for loosened transmission casing. The natural frequency and vibration mode shape are modal parameter required for initial design. The study of loose transmission casing is important for the point of view of resonance phenomena. The first 20-vibration mode shape and natural frequencies were calculated for zero displacement constraint condition, back and right side positional unconstraint conditions using FEM simulation. The study has theoretical and practical reference for the structure optimization of truck transmission casing. FEM based analysis tool ANSYS 14.5 has good analysis features and Solid Edge, Pro-E were used for modelling of transmission casing. The natural frequency of FEM simulation varies from, zero displacement condition (1669-3576) Hz, back side (1165-3467) Hz and right side (1929-3804)Hz positional unconstraint loose transmission casing. The loosening of transmission casing decrease the natural frequency by (3-30)% of zero displacement constraint condition.

FEA Based Study of Loose Transmission Gearbox Housing

Transmission gearbox housing is subjected to noise and vibration induced by internal harmonic excitation. The internal harmonic excitation produces a dynamic mesh force, which is transmitted to the housing through the shafts and bearings and causes transmission failure. The main objective of this research work is to study the relation between the transmission vibration and the positional fixed constraints of vehicle frame by comparing the free vibration results of zero displacement constraint condition to positional constraint of the different number of connecting bolts. The vehicle gearbox housing is mounted on vehicle frame using connecting bolts fixture. The present design of heavy vehicle truck transmission housing is mounted on vehicle frame using 37 connecting bolts on five different positions. The study has been completed in two parts, in first parts all 37 connecting bolts were fixed on vehicle frame and in second part of study the front and bottom positional bolts were loosened to study the relation between vibration and constraint connecting bolts. Reciprocity Principle was used to apply the loads on housing. The first 20 vibration mode shape and natural frequencies were calculated using ANSYS 14.5. The study has theoretical and practical importance for the structure optimization of gearbox housing. ANSYS 14.5 is used as FEA based analysis tool. The natural frequency for zero displacement condition varies from 1669 Hz to 3576 Hz and for loose transmission housing frequency varies from 750 Hz to 3802 Hz. The analysis results is verify with experimental results available in literature.

Introducing the sequential linear programming level-set method for topology optimization

This paper introduces an approach to level-set topology optimization that can handle multiple constraints and simultaneously optimize non-level-set design variables. The key features of the new method are discretized boundary integrals to estimate function changes and the formulation of an optimization sub-problem to attain the velocity function. The sub-problem is solved using sequential linear programming (SLP) and the new method is called the SLP level-set method. The new approach is developed in the context of the Hamilton-Jacobi type level-set method, where shape derivatives are employed to optimize a structure represented by an implicit level-set function. This approach is sometimes referred to as the conventional level-set method. The SLP level-set method is demonstrated via a range of problems that include volume, compliance, eigenvalue and displacement constraints and simultaneous optimization of non-level-set design variables.

A dynamics based two-stage path model for the docking navigation of a self-assembly modular robot (Sambot)

SUMMARYAutonomous docking is a focus of research in the field of self-assembly robots. Navigation is a significant stage in the process of autonomous docking between two robotic modules; it determines the efficiency of docking and even the success and failure of the docking task. In most cases, it is too difficult to simultaneously satisfy both linear and angular displacement constraints in a single dynamic numerical computation process. In the present paper, the navigation process is divided into two stages: first, the angular displacement constraint is satisfied, and then the linear displacement condition is fulfilled. In this way, the constraints are loosened and the difficulty of numerical computation is thereby effectively reduced. This two-stage docking navigation model is the main contribution of the present work. By taking the non-holonomic nature of the navigation behavior into consideration, both kinematic and dynamic analyses are performed, and the voltage data of the DC motors required by the two-stage docking navigation are obtained. Finally, docking navigation experiments are completed on a self-assembly modular robot named Sambot. It is verified that the present two-stage strategy is effective in controlling the docking navigation process.

Mixed-dimensional finite element coupling for structural multi-scale simulation

Multi-scale finite element (FE) modeling and analysis of engineering structures have become very necessary in order to provide both global and local structural information for a comprehensive assessment of structural safety. The multi-scale FE modeling needs FE coupling methods to combine mixed-dimensional finite elements, such as beam-to-shell and plate-to-solid, in a single structural model. This paper presents a new mixed-dimensional FE coupling method that can achieve both displacement compatibility and stress equilibrium at the interface between the different element types. The principle of virtual work is first used to derive both linear force and displacement constraint equations for the interface. A numerical method compatible with commercial FE codes is developed to figure out the linear constraint equations which satisfy both displacement compatibility and stress equilibrium conditions at the interface. The proposed coupling method is then extended to nonlinear mixed-dimensional FE coupling problems. Finally, the proposed coupling method is applied to a number of test cases including linear beam-to-plate, beam-to-shell and beam-to-solid interface problems, a linear frame structure, and a beam-to-shell buckling problem. The obtained results are also compared with those from the existing methods. It reveals that the proposed coupling method can handle both linear and nonlinear mixed-dimensional FE coupling problems more accurately than the existing methods and that it can be applied to a structure satisfactorily for multi-scale simulation.

Analysis and Optimization of Bracket of Slag Well Based on ABAQUS

This paper use Pro / E for the solid modeling of bracket of slag well firstly,Then import it into Abaqus, applied stress and displacement constraints, after calculation according to the calculation result Optimized and improved it accordingly and corresponding it.

Modeling and control of tissue compression and temperature for automation in robot-assisted surgery.

Robotic surgery is being used widely due to its various benefits that includes reduced patient trauma and increased dexterity and ergonomics for the operating surgeon. Making the whole or part of the surgical procedure autonomous increases patient safety and will enable the robotic surgery platform to be used in telesurgery. In this work, an Electrosurgery procedure that involves tissue compression and application of heat such as the coaptic vessel closure has been automated. A MIMO nonlinear model characterizing the tissue stiffness and conductance under compression was feedback linearized and tuned PID controllers were used to control the system to achieve both the displacement and temperature constraints. A reference input for both the constraints were chosen as a ramp and hold trajectory which reflect the real constraints that exist in an actual surgical procedure. Our simulations showed that the controllers successfully tracked the reference trajectories with minimal deviation and in finite time horizon. The MIMO system with controllers developed in this work can be used to drive a surgical robot autonomously and perform electrosurgical procedures such as coaptic vessel closures.

Optimization of Steel Lattice Trusses Considering Members Stability

This paper extends the optimization model of space truss finite element method to planar steel lattice truss structures under multiple constraints involved with the strength and the stability of members as well as the mid span deflection based on sequential linear programming (SLP) and affine-scale dual algorithm with the size of members as the optimization variables and the minimum weight as the optimization objective. Algorithm implemented with programming, an example of square pyramid space grid is meant for the verification of the optimization performance that the algorithm and program extends an active control to the stability and the mid span deflection as well simultaneously during optimization. Moreover, stress and deflection constraints were enlarged and reduced, the optimization results indicate that more districted constraints bring about greater ultimate steel consumption, which extends a certification to the effectiveness of the proposal optimization model to deal with all kinds of stress and displacement constraints.

A crack length control scheme for solving nonlinear finite element equations in stable and unstable delamination propagation analysis

An automatic incremental solution algorithm for nonlinear static finite element analysis of delamination propagation problems is presented. This load–displacement–constraint method iterates in the load displacement space utilizing the Newton–Raphson method, allowing to trace out the complete equilibrium path. The procedure can calculate pre- and post-critical responses of bi-dimensional problems, ranging from stable delamination growth to structural collapse by unstable growth or delamination buckling with arbitrarily sharp snap-back instabilities. Benchmark solution examples of established composite materials structural problems illustrate the effectiveness of the method.

Evolutionary topology optimization of continuum structures with a global displacement control

The conventional compliance minimization of load-carrying structures does not directly deal with displacements that are of practical importance. In this paper, a global displacement control is realized through topology optimization with a global constraint that sets a displacement limit on the whole structure or certain sub-domains. A volume minimization problem is solved by an extended evolutionary topology optimization approach. The local displacement sensitivities are derived following a power-law penalization material model. The global control of displacement is realized through multiple local displacement constraints on dynamically located critical nodes. Algorithms are proposed to secure the stability and convergence of the optimization process. Through numerical examples and by comparing with conventional stiffness designs, it is demonstrated that the proposed approach is capable of effectively finding optimal solutions which satisfy the global displacement control. Such solutions are of particular importance for structural designs whose deformed shapes must comply with functioning requirements such as aerodynamic performances.

Meshless implementation of the geometrically exact Kirchhoff–Love shell theory

SUMMARYIn the present paper, a meshless generalized multiple fixed least squares implementation of the geometrically exact Kirchhoff–Love shell theory is described. The material time derivative of the deformation gradient and the first Piola–Kirchhoff stress tensor are considered as basic conjugate quantities to evaluate the internal power. The shell's initial geometry is reproduced exactly by the predefined mapping from a reference plane configuration. As a constitutive model, a neo‐Hookean material, whose functional is altered in compliance with the plane stress condition, is chosen.The augmented weak form, suitable for both interpolative and non‐interpolative approximations thanks to the imposition of the essential boundary conditions through Lagrange multipliers, is consistently linearized, and the resultant bilinear form proved to be symmetric. The appearance of the corner reactions, related to the jumps of the pseudo‐torsion boundary moment, requires the inclusion of additional pointwise displacement constraints at the essential boundary corners. The importance of these quantities is demonstrated in the numerical tests, revealing its positive influence on the displacements and, particularly, their derivatives (up to 3rd order) in both linear and nonlinear problems.The possibility of incorporation of drilling boundary moment for nonlinear problems was successfully assessed. Copyright © 2014 John Wiley & Sons, Ltd.

Harmony search based, improved Particle Swarm Optimizer for minimum cost design of semi-rigid steel frames

This paper proposes a Particle Swarm Optimization (PSO) algorithm, which is improved by making use of the Harmony Search (HS) approach and called HS-PSO algorithm. A computer code is developed for optimal sizing design of non-linear steel frames with various semi-rigid and rigid beam-to-column connections based on the HS-PSO algorithm. The developed code selects suitable sections for beams and columns, from a standard set of steel sections such as American Institute of Steel Construction (AISC) wide-flange W-shapes, such that the minimum total cost, which comprises total member plus connection costs, is obtained. Stress and displacement constraints of AISC-LRFD code together with the size constraints are imposed on the frame in the optimal design procedure. The nonlinear moment-rotation behavior of connections is modeled using the Frye-Morris polynomial model. Moreover, the P-<TEX>${\Delta}$</TEX> effects of beam-column members are taken into account in the non-linear structural analysis. Three benchmark design examples with several types of connections are presented and the results are compared with those of standard PSO and of other researches as well. The comparison shows that the proposed HS-PSO algorithm performs better both than the PSO and the Big Bang-Big Crunch (BB-BC) methods.

An Explicit Lagrange Constraint Method for Finite Element Analysis of Frictionless 3D Contact/Impact Problems

An effective contact algorithm is essential for modeling complicated contact/impact problems. Unlike the penalty method, the Lagrange multiplier method can generate more precise results while not adversely affecting stability; however, its formulation in explicit contact treatment is singular. In order to overcome this deficiency, a new Lagrange constraint method with different constraints under initial impact and persistent contact is proposed. In this method, the coupled contact system equilibrium equations with non-diagonal coefficient matrix are uncoupled via Gauss-seidel iteration strategy. Particularly, this implicit contact treatment can be compatible with explicit time integration scheme. To reduce oscillations, the displacement constraint is imposed under initial impact, while the combined constraints of velocity, acceleration and displacement are enforced under persistent contact. Numerical example validates this method.

Topology optimization of thermoelastic structures using the guide-weight method

The guide-weight method is introduced to solve the topology optimization problems of thermoelastic structures in this paper. First, the solid isotropic microstructure with penalization (SIMP) with different penalty factors is selected as a material interpolation model for the thermal and mechanical fields. The general criteria of the guide-weight method is then presented. Two types of iteration formulas of the guide-weight method are applied to the topology optimization of thermoelastic structures, one of which is to minimize the mean compliance of the structure with material constraint, whereas the other one is to minimize the total weight with displacement constraint. For each type of problem, sensitivity analysis is conducted based on SIMP model. Finally, four classical 2-dimensional numerical examples and a 3-dimensional numerical example considering the thermal field are selected to perform calculation. The factors that affect the optimal topology are discussed, and the performance of the guide-weight method is tested. The results show that the guide-weight method has the advantages of simple iterative formula, fast convergence and relatively clear topology result.

Seismic optimal design of 3D steel frames using cuckoo search algorithm

Summary The present article is concerned with optimization of real size 3D steel structures under seismic loading based on response spectral and equivalent static analyses. The effect of lateral seismic loading distribution on the achieved optimum designs is investigated. An integrated optimization procedure with the objective of minimizing the self-weight of frame is simply performed interfacing SAP2000 and MATLAB® software in the form of parallel computing. The meta-heuristic algorithm chosen here is the cuckoo search (CS) algorithm recently developed as a type of population-based algorithm inspired by the behavior of some cuckoo species in combination with the Levy flight behavior. The CS algorithm performs suitable selection of sections from the American Institute of Steel Construction (AISC) wide-flange (W) shapes list. Strength constraints of the AISC load and resistance factor design specification, geometric limitations, and displacement constraints are imposed on the considered frames. Results show similar weights for optimum designs using spectral and equivalent static analyses; however, different material distribution and seismic behaviors are observed. Copyright © 2014 John Wiley & Sons, Ltd.

Non-linear vibration of an angular-misaligned rotor system with uncertain parameters

Parametric uncertainties play a significant role in the response predictions of a rotor system. In this paper, the quantification of uncertainty effects on the dynamic responses and vibration characteristics of a multi-rotor bearing system with the fault of angular misalignment is investigated. First, the motion equations of the rotor system are derived by taking into account the nonlinear supporting bearing and the displacement constraint between two rotors. The stochastic modeling with uncertainties of misalignment, damping and nonlinear support stiffness are then developed based on the polynomial chaos expansion technique in a stochastic framework, and traditional Monte-Carlo simulation is used as a comparison reference. Finally, the response statistics and dynamic behaviors of the stochastic system are demonstrated by mean and its probability density function (PDF). The results show that the super-harmonic resonance occur at the 1/2 of the critical speed due to the effect of misalignment, and as the uncertainty increases the realization amplitudes are spread over a wider band of amplitudes. Furthermore, P-bifurcation in the response PDFs is also presented in some situations.

Collapse optimization for domes under earthquake using a genetic simulated annealing algorithm

There are two primary collapse scenarios for single-layer latticed shells subjected to severe earthquake action: dynamic instability and strength failure. Of these, dynamic instability is the collapse scenario that must be avoided. First, taking the minimization of the standard deviation of the well-formedness as the optimization objective and the member sections as the optimization variables, an optimization model representing collapse scenarios for single-layer spherical shells is established. This optimization model also accounts for the displacement and stress constraints. Second, a genetic simulated annealing algorithm (GASA) is proposed by combining a genetic algorithm (GA) and a simulated annealing algorithm (SA). Finally, partial and overall optimizations are performed for a single-layer spherical shell that collapses due to instability under earthquake action. The results show that the optimized structure is subject to ideal strength failure under earthquake action with clear warning signs prior to collapse. In addition, the GASA performs better than the GA for optimization. Therefore, it is concluded that the optimization model and method presented in this paper can be used to perform collapse scenario optimization for single-layer spherical shells subjected to earthquake action.

Mechanism and Control of Eccentric Wear of Sucker Rod

The issue of eccentric wear of sucker rod is not only reduce the strength of the sucker rod that results to sucker rod breaking, but also wear out the pipe leading to leakage of tubing, which impact the regular production of the well. This paper aims at the popular issue in-site, analyze the factors such as wellbore deviation, stroke and fluid viscosity, tested the effect of water content, submergence on the eccentric wear by the laboratory experiment. The mechanism of eccentric wear of sucker rod is studied based on the factors impact the deformation under the stress and displacement constraints. An advanced technique is proposed to prevent eccentric wear based on the theory of hydraulic lubrication theory. It can make wedge form gap formed between sucker rod and tubing with the special tools, so that prolong the life of the well.

A topology optimization method based on element independent nodal density

A methodology for topology optimization based on element independent nodal density (EIND) is developed. Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function. The influence of the diameter of interpolation is discussed which shows good robustness. The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint. The rational approximation for material properties (RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions. Solutions are shown to meet stability, mesh dependence or non-checkerboard patterns of topology optimization without additional constraints. Finally, the computational efficiency is greatly improved by multithread parallel computing with OpenMP.

Optimal placement of steel plate shear walls for steel frames by bat algorithm

SUMMARYLayout optimization of steel frames with steel plate walls (SPWs) using a meta‐heuristic search algorithm is the main aim of the present study. SPWs are lateral load‐resisting systems, especially against earthquake excitation. These systems offer significant advantages in terms of cost, performance and ease of design compared with other systems. In this study, orthotropic membrane model is used to model the behaviour of steel plate shear walls. The newly developed bat algorithm, which is based on the echolocation behaviour of bats, is employed as the present study optimizer. Design variables of the optimization problem consist of the cross sections of beams and columns of the frame, the web plate thicknesses of SPWs and the placement of SPW in the frame. The bat algorithm performs suitable selection of sections from the AISC wide‐flange (W) shapes list. Strength constraints of the American Institute of Steel Construction Load and Resistance Factor Design and displacement constraints are checked during the optimization process. The results reveal the effectiveness of the proposed method for optimization of steel frames with SPWs. Copyright © 2014 John Wiley &amp; Sons, Ltd.