The Classical Field Theories

Linear elasticity is one of the more successful theories of mathematical physics Its pragmatic success in describing the small deformations of many materials is uncontested The origins of the three-dimensional theory go back to the beginning of the 19th century and the derivation of the basic equations by Cauchy, Navier, and Poisson The theoretical development of the subject continued at a brisk pace until the early 20th century with the work of Beltrami, Betti, Boussinesq, Kelvin, Kirchhoff, Lame, Saint-Venant, Somigliana, Stokes, and others These authors established the basic theorems of the theory, namely compatibility, reciprocity, and uniqueness, and deduced important general solutions of the underlying field equations In the 20th century the emphasis shifted to the solution of boundary-value problems, and the theory itself remained relatively dormant until the middle of the century when new results appeared concerning, among other things, Saint-Venant’s principle, stress functions, variational principles, and uniqueness

The Linear Theory of Elasticity

Free-surface flows solved by means of SPH schemes with numerical diffusive terms

A simple procedure to improve the pressure evaluation in hydrodynamic context using the SPH

Accurate characterizations of rock strengths under higher loading rates are crucial in many rock engineering applications. The split Hopkinson pressure bar (SHPB) system has been used to quantify the dynamic compressive strength of rocks using the short cylindrical specimen and the dynamic tensile strength of rocks using the Brazilian disc (BD) specimen. However, SHPB is a standard tool that is suitable for metal testing; there are some fundamental issues that need to be carefully visited in applying SHPB to rock dynamic tests. This paper addresses several such critical issues, including the choice of slenderness ratio of the compressive specimen, the effect of friction between the sample and bars on the measured results of compressive strength, the necessity of dynamic force balance on the dynamic BD test, and the validity of using the standard BD equation in the data reduction. We show that with proper experimental designs that address these issues, the dynamic compressive strength and dynamic tensile strength of rocks measured using SHPB are valid and reliable.

Some Fundamental Issues in Dynamic Compression and Tension Tests of Rocks Using Split Hopkinson Pressure Bar

On the Direct Determination of Stress in an Elastic Solid, with application to the Theory of Plates

The Inversion of Plane Stress

The Flexure of a Circular Plate

LIV. Conjectures concerning the cause, and observations upon the phænomena, of earthquakes; particularly of that great earthquake of the first of November 1775, which proved so fatal to the city of Lisbon, and whose effects were felt as far as Africa, and more or less throughout almost all Europe

The elements of mathematical analysis

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

J. H. Michell

Author Tools

Chat about Author