Joseph P. Wright

Mixed time integration schemes

Abstract A current topic of research is the development of structural dynamics codes which permit different time integration methods to be used in different parts of the structure. The primary goal of this effort is the design and implementation of more efficient solution procedures. This paper presents a review of this research and emphasizes some of the factors which are important in this work. In particular, it is shown that operator splitting methods provide a natural framework for the future development of consistent and stable mixed integration schemes

Numerical stability of a variable time step explicit method for Timoshenko and Mindlin type structures

An efficient method for calculating the transient response of Timoshenko and Mindlin type structures is to use explicit time integration combined with increased rotatory inertia. Numerical stability analysis shows that time step variations are important in determining how much to increase the inertia.

Neural Network Initialization with Prototypes - Function Approximation in Engineering Mechanics Applications

A prototype-based initialization methodology is proposed to approximate functions that are used to characterize nonlinear stress-strain, moment-curvature, and load-displacement relationships, as well as restoring forces and time histories in engineering mechanics applications. Three prototypes are defined by exploiting the capabilities of linear sums of sigmoidal functions. By using the proposed prototypes either individually or combinatorially, successful training can take place for ten specific types of nonlinear functions and far beyond when the required number of hidden nodes and initial values of weights and biases can always be derived before the training starts. Some mathematical insights to this initialization methodology and a few prototypes are offered, while training examples are provided to demonstrate a clear procedure that is used to implement this methodology. With the derived numbers of hidden nodes in each approximation, applying the Nguyen-Widrow algorithm is enabled and the training performance is compared between the existing and the proposed initialization options.

Neural network initialization with prototypes - a case study in function approximation

The initialization of neural networks in function approximation has been studied by many researchers yet remains a challenging problem. Another important yet open issue in the neural network community is to incorporate knowledge and hints with regard to training for a meaningful neural network. This study makes an attempt to address these two issues in handling a specific type of engineering problems, namely, modeling nonlinear hysteretic restoring forces of a dynamic system under a specific formulation. The paper showcases a heuristic idea on using a growing technique through a prototype-based initialization where the insights to the governing mathematics/physics are related to the features of the activation functions.

Exponentially Decaying Pressure Pulse Moving With Constant Velocity on the Surface of a Layered Elastic Material (Superseismic Layer, Subseismic Half Space)

Abstract : The response of a layered elastic half-space to a progressing exponentially decaying normal surface pressure is evaluated for a case in which the constant velocity V of the moving pressure is greater than that of the P and S waves, respectively, in the upper layer (superseismic) and smaller than these wave speeds in the underlying half-space (subseismic). It is assumed that a steady-state exists with respect to coordinate axis attached to the moving load. The superseismic-subseismic geometry results in a stress field that extends over the entire plane, with sharp shocks possible only in that portion of the layer that lies behind the front of the progressing normal loading. A computer program for evaluating stresses and velocities at points in the medium is available and results are presented for a typical configuration of interest. (Author)

Pressures in a submerged fluid-filled cylindrical shell subjected to a step wave

Abstract The response of a submerged, fluid-filled, infinitely long, cylindrical shell (plane-strain ring) subjected to a step shock wave is studied to determine the effect of shell parameters (moduli, thickness, radius) on the shape of the pressure pulse transmitted inside the shell. The results show that the shell is transparent if thin enough, but, as the thickness increases, strong shell vibrations become important and distort the pulse.

Solving Dynamical Systems Involving Piecewise Restoring Force Using State Event Location

Abstract Many theoretical and experimental studies of complex path-dependent dynamic systems lead to restoring forces expressed as piecewise nonlinear algebraic equations. Examples include, but are not limited to, bilinear hysteretic, Ramberg-Osgood, Masing, generalized Masing, Clough, and Takeda models, which are popular in engineering mechanics applications. These models relate restoring force to displacement and velocity by means of piecewise relations having only C0 continuity, which leads to two sorts of challenges in numerical simulation. First, the equations of motion may not simply be a set of ordinary differential equations, rather they may fall within the framework of differential-algebraic equations (DAEs). Second, there are unknown locations of discontinuities of low-order derivatives of the solution. This study seeks accurate and efficient numerical solutions of the DAEs with C0 continuity, enabling robust simulation of these complex nonlinear dynamic systems. This study focuses on explicit t...

Embedded EMD algorithm within an FPGA-based design to classify nonlinear SDOF systems

Compared with traditional microprocessor-based systems, rapidly advancing field-programmable gate array (FPGA) technology offers a more powerful, efficient and flexible hardware platform. An FPGA and microprocessor (i.e., hardware and software) co-design is developed to classify three types of nonlinearities (including linear, hardening and softening) of a single-degree-of-freedom (SDOF) system subjected to free vibration. This significantly advances the teams previous work on using FPGAs for wireless structural health monitoring. The classification is achieved by embedding two important algorithms - empirical mode decomposition (EMD) and backbone curve analysis. Design considerations to embed EMD in FPGA and microprocessor are discussed. In particular, the implementation of cubic spline fitting and the challenges encountered using both hardware and software environments are discussed. The backbone curve technique is fully implemented within the FPGA hardware and used to extract instantaneous characteristics from the uniformly distributed data sets produced by the EMD algorithm as presented in a previous SPIE conference by the team. An off-the-shelf high-level abstraction tool along with the MATLAB/Simulink environment is utilized to manage the overall FPGA and microprocessor co-design. Given the limited computational resources of an embedded system, we strive for a balance between the maximization of computational efficiency and minimization of resource utilization. The value of this study lies well beyond merely programming existing algorithms in hardware and software. Among others, extensive and intensive judgment is exercised involving experiences and insights with these algorithms, which renders processed instantaneous characteristics of the signals that are well-suited for wireless transmission.

Duality of energy absorption and inertial effects: Optimized structural design for blast loading

This article provides insights into the dynamic response and protection capacity of sacrificial structures mounted on a structural member and subjected to close standoff blast loading. The three main objectives of this study are: (a) exploration of key parameters governing the failure modes of a structural member protected by a sacrificial structure; (b) quantification of blast resistance and protection capacity of the sacrificial structure and underlying structure; and (c) conducting comparative single-degree-of-freedom system analysis and high-resolution explicit finite element analysis aiming at improving current single-degree-of-freedom analysis approaches. Energy absorption and momentum resistance are identified and quantified as the main contributing mechanisms controlling the dynamic response of structural members subjected to high-speed dynamic loading. The displacement of the structural member in the blast direction, the mass per length of the structural member, and the maximum impulse are found to be parameters governing the nonlinear response. The article also presents a response surface approach which might have value for time-efficient optimized structural member design and prediction of nonlinear structural member response to blast loading. This study includes validation of the numerical data through free-air blast test data from the literature.

Mapping some functions and four arithmetic operations to multilayer feedforward neural networks

This paper continues the development of a heuristic initialization methodology for designing multilayer feedforward neural networks aimed at modeling nonlinear functions for engineering mechanics applications as presented previously at SPIE 2003, and 2005 to 2007. Seeking a transparent and domain knowledge-based approach for neural network initialization and result interpretation, the authors examine the efficiency of linear sums of sigmoidal functions while offering constructive methods to approximate functions in engineering mechanics applications. This study provides details and results of mapping the four arithmetic operations (summation, subtraction, multiplication, division) as well as other functions including reciprocal, Gaussian and Mexican hat functions into multilayer feedforward neural networks with one hidden layer. The approximation and training examples demonstrate the efficiency and accuracy of the proposed mapping techniques and details. Future work is also identified. This effort directly contributes to the further extension of the proposed initialization procedure in that it opens the door for the approximation of a wider range of nonlinear functions.