Steady-state creep analysis of polymer matrix composites using complex variable method

2013 ◽  
Vol 227 (10) ◽  
pp. 2182-2194 ◽  
Author(s):  
Vahid Monfared ◽  
Mehdi Mondali ◽  
Ali Abedian
Keyword(s):  
Steady State ◽  
Complex Variable ◽  
Analytical Method ◽  
Polymer Matrix Composites ◽  
Short Fiber ◽  
Steady State Creep ◽  
Complex Variable Method ◽  
Variable Method ◽  
Elastic Behavior ◽  
Matrix Composites

A new analytical formulation is presented to study the steady-state creep in short fiber composites using complex variable method. In this new approach, both the fiber and matrix creep at low stresses and temperatures. To analyze the crept fiber, a plane stress model was used. Important novelties of the present analytical method are determination of displacement rates with proper boundary conditions in the crept fibers and also using the complex variable method in creep analyzing. It is noteworthy that the method can be useful to study the creep behavior in polymeric matrix composites due to their high capability of creep. Moreover, another significant application of the present method is to study on the creep or elastic behavior of carbon nanotube polymer composites. Finally, the results obtained from the present analytical method (complex variable method) show a good agreement with the existing experimental results.

scholarly journals Computational modeling of creep in complex plane for reinforced materials

2017 ◽  
Vol 65 (6) ◽  
pp. 909-916
Author(s):  
V. Monfared
Keyword(s):  
Computational Modeling ◽  
Complex Plane ◽  
Complex Variable ◽  
Elevated Temperatures ◽  
Plane Stress State ◽  
Short Fiber ◽  
Complex Variable Method ◽  
Variable Method ◽  
Governing Equations ◽  
Reinforced Materials

AbstractComputational modeling for predicting the steady state creep behavior is presented in complex plane for reinforced materials by complex variable method. Both the fiber and matrix simultaneously creep at elevated temperatures and loading. We suppose that one dimension of the short fiber is small enough in comparison with the other two (see Fig. 1). In this formulation, plane stress state is used. Finally, displacement rate behaviors are predicted using compatibility, equilibrium, constitutive, and governing equations by complex variable method. One of the considerable applications of the method is in nano-composites analysis in elasticity or plasticity research.

Improved Sensitivity and Reliability Analysis of Nonlinear Euler-Bernoulli Beam Using a Complex Variable Semi-Analytical Method

2009 ◽  
Author(s):  
Weiya Jin ◽  
Brian H. Dennis ◽  
Bo Ping Wang
Keyword(s):  
Finite Element ◽  
Complex Variable ◽  
Analytical Method ◽  
Limit State ◽  
Complex Variable Method ◽  
Variable Method ◽  
State Function ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam ◽  
Accuracy Problem

The semi-analytical method (SAM) has been reported serious accuracies in sensitivity analysis of structural elements such as frame, beam, plate elements because the finite difference method (FDM) used in the SAM is sensitive to the step size. The proposed semi-analytical complex variable method (SACVM) adopts the complex variable method (CVM) to avoid the accuracy problem and maintain the computational efficiency of the SAM. Various methods have been developed to improve the accuracy of the SAM in linear structural problems. However, a few methods address this accuracy problem for nonlinear cases. The paper applies the SACVM to a geometrical nonlinear Euler-Bernoulli beam to obtain the accurate sensitivity of finite element response. As an example application, the SACVM sensitivities are used to compute the reliability index of a defined limit state function for the nonlinear beam. The results reveal that the SACVM can always compute response sensitivity and system reliability consistently, accurately and efficiently. The method is also computationally efficient as it employs a semi-analytical approach. The SACVM is easily applicable and only requires minor modifications to existing finite element codes, therefore it has great application in practical problems.

Complex Variable Method for Eigensolution Sensitivity Analysis

AIAA Journal ◽  
2006 ◽  
Vol 44 (12) ◽  
pp. 2958-2961 ◽  
Author(s):  
B. P. Wang ◽  
A. P. Apte
Keyword(s):  
Sensitivity Analysis ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method

On Bending of a Flat Slab Supported by Square-Shaped Columns and Clamped

1954 ◽  
Vol 21 (3) ◽  
pp. 263-270
Author(s):  
S. Woinowsky-Krieger
Keyword(s):  
Stress Distribution ◽  
Conformal Mapping ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method ◽  
Flat Slab ◽  
Flat Slabs ◽  
At Will

Abstract A solution is given in this paper for the problem of bending of an infinite flat slab loaded uniformly and rigidly clamped in square-shaped columns arranged to form the square panels of the slab. The complex variable method in connection with conformal mapping is used for this aim. Although not perfectly rigorous, the solution obtained is sufficiently accurate for practical purposes and, besides, it can be improved at will. Stress diagrams traced in a particular case of column dimensions do not wholly confirm the stress distribution, generally accepted in design of flat slabs.

The Stresses in a Thick Cylinder Having a Square Hole Under Concentrated Loading

1958 ◽  
Vol 25 (4) ◽  
pp. 571-574
Author(s):  
Masaichiro Seika
Keyword(s):  
Stress Distribution ◽  
Complex Variable ◽  
Complex Variable Method ◽  
Variable Method ◽  
Numerical Examples ◽  
Concentrated Loading ◽  
Thick Cylinder ◽  
Square Hole

Abstract This paper contains a solution for the stress distribution in a thick cylinder having a square hole with rounded corners under the condition of concentrated loading. The problem is investigated by the complex-variable method, associated with the name of N. I. Muskhelishvili. The unknown coefficients included in the solution are determined by the method of perturbation. Numerical examples of the solution are worked out and compared with the results available.

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