Ordinary differential equations of the first order linear differential equations complex numbers and linear algebra simultaneous linear differential equations numerical methods the descriptive theory of nonlinear differential equations mechanical systems and electric circuits Fourier series Fourier integrals and Fourier transforms the Laplace transformation partial differential equations Bessel functions and Legendre polynomials applications and further properties of matrices vector analysis the calculus of variations analytic functions of a complex variable infinite series in the complex plane the theory of residues conformal mapping.

Advanced Engineering Mathematics. By C. R. Wylie. Pp. xiv, 813. 1966. (McGraw-Hill.)

The paper focuses on the moire phenomenon as a tool of experimental mechanics. The properties of moire patterns are outlined. The application of these properties to the measurement of displacements of the points of a surface (intrinsic moire), contours or deflections (projection moire) and slopes (reflection moire) is discussed. Observation methods, recording methods, data-processing techniques are outlined and practical aspects are stressed. Sensitivities and precisions that have been achieved are reviewed. Finally, some typical applications to problems in areas of interest are briefly described.

The moiré method—A review

High-speed films recorded from head on collision tests with cadavers have been analysed with respect to the angular acceleration and angular velocity which were evaluated with Smoothed Cubic-Spline Functions. These results compared with the autopsy findings in these cases and data from studies on angular acceleration to the head of squirrel monkeys carried out by Unterharnscheidt and Higgins indicate the bridging vein disruption due to rotational movement of the head is obtained when the angular acceleration exceeds 4500 rad/sec2 and/or the change in angular velocity exceeds 50 rad/sec. These tolerance levels are compared with data from collision experiments on living human beings.

Strain tolerance of the vv. cerebri sup. (bridiging veins) calculated from head-on collision tests with cadavers.

A new smooth two-dimensional numerical method is presented for representing and differentiating discrete fullfield experimental information. The method involves minimizing a positive definite functional by use of finite-elements to ‘best-fit’ the data. Experimental data points may occur in any configuration, boundary derivatives need not be specified, and arbitrarily shaped regions can be handled readily. The method is demonstrated by photomechanical strain analysis.

Smooth spline-like finite-element differentiation of full-field experimental data over arbitrary geometry

Continuous full-field representation and differentiation of three-dimensional experimental vector data

The smoothed spline is presented as a method for obtaining high-quality derivatives in experimental-mechanics problems. The smoothed spline is discussed and methods for controlling the amount of smoothing and for avoiding derivative approximation deficiencies at the spline boundaries are presented. Applications are examined for scattered-light photoelasticity and the bending of beams.

Obtaining Derivatives from Experimental Data Using Smoothed-spline Functions The smoothed cubic spline is presented for use in obtaining high-quality derivatives from experimental data and example applications are shown for scattered-light photoelasticity and the bending of beams

J. P. Cannon

Papers

Obtaining Derivatives from Experimental Data Using Smoothed-spline Functions The smoothed cubic spline is presented for use in obtaining high-quality derivatives from experimental data and example applications are shown for scattered-light photoelasticity and the bending of beams