Optimization Of Linearly Distributed Pre-stress
In Laminated Cylinders
Author(s)
P. Procházka
Abstract
Recently the author published several papers on optimal pre-stress of laminated
composites with lamina-wise uniform distribution of pre-stresses. The result of
such an approach leads to the uniform distribution of stresses through the
thickness of the structure under consideration (laminar hollow cylinders, plates,
etc.). It appears from practical application that in the case of hollow laminar
cylinders the distribution of pre-stresses is rather linear and it is more appropriate
to consider such a type of pre-stressing. In order to express the pre-stressing,
eigenparameters are used. They were recently applied to different types of
structures and they have been introduced as a generalization of Transformation
Field Analysis, established by G. J. Dvorak from RPI, Troy, USA. The
generalization was carried out by Dvorak and the author of this paper.
1 Introduction
Recently, the author with coauthors have published several papers, e.g. [2], [4],
on optimization of stresses controlled by an appropriate choice of
eigenparameters in certain sense (plain optimization, the optimization of
reinforcing pre-stresses, the lay-ups and pre-stressing). These optimizations were
mostly connected with minimization of the variance of stresses acting in some
directions, cf. a simple example in Appendix, when the tools of the
Transformation field analysis, [1], were employed. Extended Hashin-Shtrikman
variational principles were applied and enabled one to consider anisotropic and
non-homogeneous bodies, [3].
The method from the numerical point of view leads to a linear system of
equations for unconstrained problem and when restrictions are imposed on the
stresses a nonlinear problem is to be solved. The solution of such systems is
Keywords
Related Book
Other papers in this volume
Warning (2)
: foreach() argument must be of type array|object, null given [in
/var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/templates/Papers/view.php, line
364]
Code
$counter = '0';
foreach ($paper['book']['Paper'] as $otherPaper) {
if ((!empty($otherPaper['name'])) && ($counter < '7') && ($otherPaper['available'] == 1)) {
Cake\Error\ErrorTrap->handleError() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/templates/Papers/view.php, line 364
/var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php, line 1188
Cake\View\View->_evaluate() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php, line 1145
Cake\View\View->_render() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/View/View.php, line 785
Cake\View\View->render() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/Controller.php, line 712
Cake\Controller\Controller->render() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/Controller.php, line 516
Cake\Controller\Controller->invokeAction() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/ControllerFactory.php, line 166
Cake\Controller\ControllerFactory->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Controller/ControllerFactory.php, line 141
Cake\Controller\ControllerFactory->invoke() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/BaseApplication.php, line 362
Cake\Http\BaseApplication->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 86
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Middleware/CsrfProtectionMiddleware.php, line 169
Cake\Http\Middleware\CsrfProtectionMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Middleware/BodyParserMiddleware.php, line 157
Cake\Http\Middleware\BodyParserMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Routing/Middleware/RoutingMiddleware.php, line 118
Cake\Routing\Middleware\RoutingMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Routing/Middleware/AssetMiddleware.php, line 69
Cake\Routing\Middleware\AssetMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Error/Middleware/ErrorHandlerMiddleware.php, line 115
Cake\Error\Middleware\ErrorHandlerMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/debug_kit/src/Middleware/DebugKitMiddleware.php, line 60
DebugKit\Middleware\DebugKitMiddleware->process() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 82
Cake\Http\Runner->handle() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Runner.php, line 60
Cake\Http\Runner->run() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/vendor/cakephp/cakephp/src/Http/Server.php, line 104
Cake\Http\Server->run() /var/www/dce7ae55-385b-4ffa-8595-3ec5e61ff110/public_html/app/webroot/index.php, line 37
[main]
