On the symplectic superposition method for free vibration of rectangular thin plates with mixed boundary constraints on an edge

A novel symplectic superposition method has been proposed and developed for plate and shell problems in recent years.The method has yielded many new analytic solutions due to its rigorousness.In this study,the first endeavor is made to further developed the symplectic superposition method for the free vibration of rectangular thin plates with mixed boundary constraints on an edge.The Hamiltonian system-based governing equation is first introduced such that the mathematical techniques in the symplectic space are applied.The solution procedure incorporates separation of variables,symplectic eigen solution and superposition.The analytic solution of an original problem is finally obtained by a set of equations via the equivalence to the superposition of some elaborated subproblems.The natural frequency and mode shape results for representative plates with both clamped and simply supported boundary constraints imposed on the same edge are reported for benchmark use.The present method can be extended to more challenging problems that cannot be solved by conventional analytic methods.

Corner block list representation and its application with boundary constraints

Floorplanning is a critical phase in physical design of VLSI circuits. The stochastic optimization method is widely used to handle this NP-hard problem. The key to the floorplanning algorithm based on stochastic optimization is to encode the floorplan structure properly. In this paper, corner block list (CBL)-a new efficient topological representation for non-slicing floorplan-is proposed with applications to VLSI floorplan. Given a corner block list, it takes only linear time to construct the floorplan. In floorplanning of typical VLSI design, some blocks are required to satisfy some constraints in the final packing. Boundary constraint is one kind of those constraints to pack some blocks along the pre-specified boundaries of the final chip so that the blocks are easier to be connected to certain I/O pads. We implement the boundary constraint algorithm for general floorplan by extending CBL. Our contribution is to find the necessary and sufficient characterization of the blocks along the boundary represented by CBL. We can check the boundary constraints by scanning the intermediate solutions in linear time during the simulated annealing process and fix the corner block list in case the constraints are violated. The experiment results are demonstrated by several examples of MCNC benchmarks and the performance is remarkable.

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions.However,material identification is a challenging task,especially when the characteristic of the material is highly nonlinear in nature,as is common in biological tissue.In this work,we identify unknown material properties in continuum solid mechanics via physics-informed neural networks(PINNs).To improve the accuracy and efficiency of PINNs,we develop efficient strategies to nonuniformly sample observational data.We also investigate different approaches to enforce Dirichlet-type boundary conditions(BCs)as soft or hard constraints.Finally,we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space.The estimated material parameters achieve relative errors of less than 1%.As such,this work is relevant to diverse applications,including optimizing structural integrity and developing novel materials.

Effects of Joint Controller on Analytical Modal Analysis of Rotational Flexible Manipulator

Modal analysis is a fundamental and important task for modeling and control of the flexible manipulator. However, almost all of the traditional modal analysis methods view the flexible manipulator as a pure mechanical structure and neglect feedback action of joint controller. In order to study the effects of joint controller on the modal analysis of rotational flexible manipulator, a closed-loop analytical modal analysis method is proposed. Firstly, two exact boundary constraints, namely servo feedback constraint and bending moment constraint, are derived to solve the vibration partial differential equation. It is found that the stiffness and damping gains of joint controller are both included in the boundary conditions, which lead to an unconventional secular term. Secondly, analytical algorithm based on Ritz approach is developed by using Laplace transform and complex modal approach to obtain the natural frequencies and mode shapes. And then, the numerical simulations are performed and the computational results show that joint controller has pronounced influence on the modal parameters： joint controller stiffness reduces the natural frequency, while joint controller damping makes the shape phase non-zero. Furthermore, the validity of the presented conclusion is confirmed through experimental studies. These findings are expected to improve the performance of dynamics simulation systems and model-based controllers.

Research on an Algorithm of Shape from Shading

Shape from shading(SFS)is an important domain in computer vision.The paper presented an improved algorithm of shape from shading based on a single image according to an existed one.The presented algorithm enhanced the boundary constraints to eliminate the rotation distortion on the border of reconstructed object and introduced the factor of brightness error to weaken the influence irradiance equation’s nonlinearity on reconstructed errors.The reconstructed results verify the performance improvement in terms of accuracy by the input image of a synthetic image and a real image of weld.

Un-thorough Delaunay Approach for Tetrahedral Mesh Generation

An integrated tetrahedrization algorithm in 3D domain which combines the Delaunay tetrahedral method with un-Delaunay tetrahedral method is described. The algorithm was developed by constructing Delaunay Tetrahedrons from a scattered point set, recovering boundaries using Delaunay and un-Delaunay method, inserting additional nodes in unsuitable tetrahedrons, optimizing tetrahedrons and smoothing the tetrahedral mesh with the 2D-3D Laplacian method. The algorithm has been applied to the injection molding CAE preprocessing.

Constrained multi-degree reduction of triangular Bézier surfaces

This paper proposes and applies a method to sort two-dimensional control points of triangular Bezier surfaces in a row vector. Using the property of bivariate Jacobi basis functions, it further presents two algorithms for multi-degree reduction of triangular Bezier surfaces with constraints, providing explicit degree-reduced surfaces. The first algorithm can obtain the explicit representation of the optimal degree-reduced surfaces and the approximating error in both boundary curve constraints and corner constraints. But it has to solve the inversion of a matrix whose degree is related with the original surface. The second algorithm entails no matrix inversion to bring about computational instability, gives stable degree-reduced surfaces quickly, and presents the error bound. In the end, the paper proves the efficiency of the two algorithms through examples and error analysis.

Optimal multi-degree reduction of C-Bezier surfaces with constraints

We propose an optimal approach to solve the problem of multi-degree reduction of C-Brzier surfaces in the norm L2 with prescribed constraints. The control points of the degree-reduced C-Brzier surfaces can be explicitly obtained by using a matrix operation that is based on the transfer matrix of the C-Brzier basis. With prescribed boundary constraints, this method can be applied to piecewise continuous patches or to a single patch with the combination of surface subdivision. The resulting piecewise approximating patches are globally G1 continuous. Finally, numerical examples are presented to show the effectiveness of the method.

Dynamic Behavior and Vibration Suppression of a Generally Restrained Pre-pressure Beam Structure Attached with Multiple Nonlinear Energy Sinks

Beam structures are extensively used in many engineering branches.For marine engineering,the ship shafting system is generally simplified as a vibration model with single or multiple beam structures connected by the coupling stiffness.In engineering,multiple nonlinear energy sinks(NESs)can be arranged on the premise of sufficient installation space to ensure their vibration suppression effect.Considering engineering practice,this study investigates the dynamic behavior and vibration suppression of a generally restrained pre-pressure beam structure with multiple uniformly distributed NESs,where the prepressure is typically caused by thrust bearings,installation ways,and others.System governing equations are derived through the generalized Hamiltonian principle and the variational procedure.Dynamic responses of the pre-pressure beam structure are predicted by the Galerkin truncation method.The effect of NESs on dynamic responses and vibration suppression of the pre-pressure beam structure is studied and discussed.Suitable parameters of NESs have a beneficial effect on the vibration suppression at both ends of the pre-pressure beam structure.NESs can modify the vibration frequency and energy transmission characteristics of the vibration system.For different boundary conditions,the optimized parameters of NESs significantly suppress the vibration energy of the pre-pressure beam structure.