THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

A critical review of recent research on functionally graded plates

SLM lattice structures: Properties, performance, applications and challenges

THE appearance of a treatise in English upon the mathematical theory of elasticity is an event the potential importance of which may be judged by the that the author, in his frequent suggestions for collateral reading, refers to only three such, those of Southwell, Timoshenko, and Love. In spirit and content Sokolnikoff}s book differs greatly from each and all of these. It may be described by a possible sub-title: “A pure mathematician surveys topics related to certain problems in the mathematical theory of elasticity”. It is symptomatic of the change in outlook of American mathematics over the past few decades. Mathematical Theory Of Elasticity Prof. I. S. Sokolnikoff with the collaboration of Asst. Prof. R. D. Speche. Pp. xi + 373. (New York and London: McGraw-Hill Book Co., Inc., 1946.) 22s. 6d.

Mathematical Theory Of Elasticity

Metal additive manufacturing in aerospace: A review

The present work evaluates the effect of thickness stretching in plate/shell structures made by materials which are functionally graded (FGM) in the thickness directions. That is done by removing or retaining the transverse normal strain in the kinematics assumptions of various refined plate/shell theories. Variable plate/shell models are implemented according to Carrera’s Unified Formulation. Plate/shell theories with constant transverse displacement are compared with the corresponding linear to fourth order of expansion in the thickness direction ones. Single-layered and multilayered FGM structures have been analyzed. A large numerical investigation, encompassing various plate/shell geometries as well as various grading rates for FGMs, has been conducted. It is mainly concluded that a refinements of classical theories that include additional in-plane variables could results meaningless unless transverse normal strain effects are taken into account.

Effects of thickness stretching in functionally graded plates and shells

A large variety of plate theories are described and assessed in the present work to evaluate the bending and vibration of sandwich structures. A brief survey of available works is first given. Such a survey includes significant review papers and latest developments on sandwich structure modelings. The kinematics of classical, higher order, zigzag, layerwise, and mixed theories is described. An exhaustive numerical assessment of the whole theories is provided in the case of closed form solutions of simply supported panels made of orthotropic layers. Reference is made to the unified formulation that has recently been introduced by the first author for a plate/shell analysis. Attention has been given to displacements, stresses (both in-plane and out-of-plane components), and the free vibration response. Only simply supported orthotropic panels loaded by a transverse distribution of bisinusoidal pressure have been analyzed. Five benchmark problems are treated. The accuracy of the plate theories is established with respect to the length-to-thickness-ratio (LTR) geometrical parameters and to the face-to-core-stiffness-ratio (FCSR) mechanical parameters. Two main sources of error are outlined, which are related to LTR and FCSR, respectively. It has been concluded that higher order theories (HOTs) can be conveniently used to reduce the error due to LTR in thick plate cases. But HOTs are not effective in increasing the accuracy of the classical theory analysis whenever the error is caused by increasing FCSR values; layerwise analysis becomes mandatory in this case.

A Survey With Numerical Assessment of Classical and Refined Theories for the Analysis of Sandwich Plates

Smart structures that contain embedded piezoelectric patches are loaded by both mechanical and electrical fields. Traditional plate and shell theories were developed to analyze structures subject to mechanical loads. However, these often fail when tasked with the evaluation of both electrical and mechanical fields and loads. In recent years more advanced models have been developed that overcome these limitations. Plates and Shells for Smart Structures offers a complete guide and reference to smart structures under both mechanical and electrical loads, starting with the basic principles and working right up to the most advanced models. It provides an overview of classical plate and shell theories for piezoelectric elasticity and demonstrates their limitations in static and dynamic analysis with a number of example problems. This book also provides both analytical and finite element solutions, thus enabling the reader to compare strong and weak solutions to the problems.

Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis

This work addresses the static analysis of functionally graded material plates subjected to transverse mechanical loadings. The unified formulation and principle of virtual displacements are employed to obtain both closed-form and finite element solutions. The use of the unified formulation permits a large variety of plate models with variable kinematic assumptions to be compared in the same framework. These differ according to the order of the expansion in the thickness direction and the variable description: the order of the expansion ranges from 1 to 4, thus covering first-order as well as higher-order theories; the description of the unknowns can be equivalent single layer or layerwise. The dependence of the material data on the thickness direction was introduced by employing thickness functions that are derived from the Legendre polynomials that are used in the layerwise case. The proposed approach is independent of the used transition function, and as a result, any continuous variations of the material properties in the thickness direction may be easily implemented. The obtained solutions (closed form and finite element) are validated through comparison with three-dimensional exact solutions and other available solutions. These show the limitations of classical plate theories as well as the convenience of the use of the proposed variable kinematic models for the analysis of functionally graded material plates.

Salvatore Brischetto

Papers

Effects of thickness stretching in functionally graded plates and shells

A Survey With Numerical Assessment of Classical and Refined Theories for the Analysis of Sandwich Plates

Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis

Variable Kinematic Model for the Analysis of Functionally Graded Material plates

Analysis of thickness locking in classical, refined and mixed multilayered plate theories