From 852e96567b8821489f9a858d8a01f75a6908462a Mon Sep 17 00:00:00 2001 From: "Denis V. Dedkov" Date: Sat, 21 Jun 2014 17:38:04 +0600 Subject: [PATCH] Fragment slice was redrawed, table was modified --- c2.tex | 17 +++++- c3.tex | 99 +++++++++----------------------- disser.kilepr | 78 +++++++++++++++++-------- fig/geometry/fragment_slice.png | Bin 0 -> 269390 bytes stress_concentartors.tex | 4 +- tables/p0s0.csv | 8 +++ 6 files changed, 109 insertions(+), 97 deletions(-) create mode 100644 fig/geometry/fragment_slice.png create mode 100644 tables/p0s0.csv diff --git a/c2.tex b/c2.tex index 7ce9ed8..5ffaae7 100644 --- a/c2.tex +++ b/c2.tex @@ -58,6 +58,21 @@ bib:salome:additional_geom, bib:laduga:geom}. далее оси $x_1$ и $x_3$ ортогональной декартовой системы координат принадлежат плоскости слоя. +Будем рассматривать случаи, когда между волокнами основы и утка присутствует +гарантированная просолойка матрицы~(рис.~\ref{fig:c2:fragment_slice}~а) либо +волокна основы и утка соприкасаются в местах наибольших кривизн, в следствие +чего возникает наличие площадки контакта между +волокнами~(рис.~\ref{fig:c2:fragment_slice}~б). + +\begin{figure}[ht] + \centering + \includegraphics[width=0.7\linewidth]{geometry/fragment_slice} + \caption{Срез фрагмента слоя тканого композита с идеальной периодической +структурой: а)~волокна окружены гарантированной прослойкой матрицы, б)~наличие +площадки контакта между волокнами.} + \label{fig:c2:fragment_slice} +\end{figure} + Будем рассматривать дефекты, типичные для тканых композитов с поликристаллической матрицей: пропуск нити основы (рис.~\ref{fig:c2:fiber_skip}), разрыв волокна основы @@ -271,7 +286,7 @@ C_{ijkl}^{m} \left[ 1-\lambda({\bf r}) \right ] \right\} \begin{figure}[ht!] \centering - \includegraphics[width=17cm]{mesh/v1/matrix} + \includegraphics[width=15cm]{mesh/v2/matrix} \caption{Пример дискретизации матрицы} \label{fig:mesh:matrix} \end{figure} diff --git a/c3.tex b/c3.tex index e1e8fdb..210c26f 100644 --- a/c3.tex +++ b/c3.tex @@ -1,11 +1,35 @@ +\pgfplotstableset{ + col sep=comma, + use comma, + every head row/.style={before row=\hline,after row=\hline\hline}, + every last row/.style={after row=\hline}, + every nth row={1}{before row=\hline}, + every nth row={2}{before row=\hline\hline}, + columns={type,ksxx,ksyy,kszz,ksxy,ksxz,ksyz}, + columns/type/.style={column name=Тип дефекта, + column type=|p{8cm}|, + string type}, + columns/ksxx/.style={column name=$K_{\sigma_{11}}$, + column type=|c}, + columns/ksyy/.style={column name=$K_{\sigma_{22}}$, + column type=|c}, + columns/kszz/.style={column name=$K_{\sigma_{33}}$, + column type=|c}, + columns/ksxy/.style={column name=$K_{\sigma_{12}}$, + column type=|c}, + columns/ksxz/.style={column name=$K_{\sigma_{13}}$, + column type=|c}, + columns/ksyz/.style={column name=$K_{\sigma_{23}}$, + column type=|c|} +} + \chapter{Математическая модель слоя тканого композиционного материала с искривленными волокнами и внутренними технологическими дефектами} В главе\inthirdtext \section{Математическая модель упруго-хрупкого поведения слоя тканого композита -с поликристаллической матрицей при наличии гарантированной прослойки матрицы -между волокнами} +c керамическими волокнами и поликристаллической матрицей} \subsection{Коэффициенты концентрации напряжений} @@ -16,41 +40,7 @@ \centering \caption{Максимальные коэффициенты концентрации напряжений в слое тканого композита при двухосном равнокомпонентном растяжении в плоскости слоя} - \begin{tabular}{|p{8cm}||c|c|c|c|c|c|} - \hline - & $K_{\sigma_{11}}$ - & $K_{\sigma_{22}}$ - & $K_{\sigma_{33}}$ - & $K_{\sigma_{12}}$ - & $K_{\sigma_{13}}$ - & $K_{\sigma_{23}}$ \\ - \hline - \hline - Пропуск волокна основы - & $1{,}36$ & $1{,}15$ & $1{,}07$ & $1{,}18$ & $1{,}05$ & $1{,}48$ \\ - \hline - Пропуск волокна основы (доуплотнение) - & $1{,}21$ & $1{,}19$ & $0{,}97$ & $0{,}99$ & $1{,}04$ & $1{,}15$ \\ - \hline - \hline - Разрыв нити основы - & $1{,}47$ & $2{,}33$ & $1{,}71$ & $0{,}97$ & $1{,}96$ & $1{,}47$ \\ - \hline - Разрыв нити основы (доуплотнение) - & $1{,}29$ & $1{,}13$ & $0{,}94$ & $1{,}16$ & $1{,}27$ & $1{,}24$ \\ - \hline - \hline - Разрыв нитей основы и утка - & $1{,}32$ & $1{,}09$ & $0{,}96$ & $0{,}95$ & $2{,}90$ & $1{,}55$ \\ - \hline - Разрыв нитей основы и утка (доуплотнение) - & $1{,}18$ & $0{,}98$ & $0{,}9$ & $1{,}01$ & $1{,}06$ & $1{,}14$ \\ - \hline - \hline - Внутренняя пора - & $1{,}08$ & $1{,}39$ & $1{,}11$ & $1{,}89$ & $1{,}27$ & $1{,}38$\\ - \hline - \end{tabular} + \pgfplotstabletypeset{tables/p0s0.csv} \label{tab:max_k_s1} \end{table} @@ -386,32 +376,11 @@ $\sigma_{13}$ и $\sigma_{23}$ и нормальная составляющая \section{Математическая модель упруго-хрупкого поведения слоя тканого композита с -поликристаллической матрицей при наличии контакта с трением между волокнами} +металическими волокнами и поликристаллической матрицей} \subsection{Геометрическая модель слоя тканого композита с контактом между волокнами} -Геометрические параметры модели аналогичны указанным в -разделе~\ref{c1:geometry}, за исключением того что расстояние между волокнами в -точках максимальных кривизн равно нулю (рис.~\ref{fig:c3:fibers}), а в матрице, -вблизи максимальных кривизн волокон всегда присутствуют внутренние -технологические поры из-за невозможности заполнить это пространство материалом -матрицы (рис.~\ref{fig:c3:matrix}). - -\begin{figure}[ht] - \includegraphics[width=17cm]{geometry/v2/regular_slice} - \caption{Фрагмент слоя ткани с контактом между волокнами} - \label{fig:c3:fibers} -\end{figure} - -\begin{figure}[ht!] - \centering - \includegraphics[width=10cm]{geometry/v2/matrix} - \caption{Фрагмент поликристаллической матрицы слоя тканого композита с -внутренними технологическими порами} - \label{fig:c3:matrix} -\end{figure} - В качестве дефектов, вызывающих концентрации напряжений будем рассматривать типичные дефекты, возникающие вследствие очень плотного расположения волокон --- разрыв волокна основы (рис.~\ref{fig:c3:d1d3}~а) и разрывы волокон основы и @@ -447,18 +416,6 @@ $\sigma_{13}$ и $\sigma_{23}$ и нормальная составляющая тканого композита. Параметры сеток, удовлетворяющих этим условиям показаны в таблице. -\begin{figure}[ht] - \includegraphics[width=17cm]{mesh/v2/matrix} - \caption{Пример дискретизации матрицы} - \label{fig:c3:mesh:matrix} -\end{figure} - -\begin{figure}[ht!] - \includegraphics[width=15cm]{mesh/v2/fibers} - \caption{Пример дискретизации волокон} - \label{fig:c3:mesh:fibers} -\end{figure} - Решив задачу \ref{eq:Eqvilibrium}~--~\ref{eq:Koshi} с граничными условиями \ref{eq:b_cond}~--~\ref{eq:b_cond_Colomb_2} методом конечных элементов получим поля интенсивностей напряжений в искривленных нитях основы и утка слоя diff --git a/disser.kilepr b/disser.kilepr index 26e8f29..bc43eb5 100644 --- a/disser.kilepr +++ b/disser.kilepr @@ -37,7 +37,7 @@ Mode=LaTeX ReadWrite=true [document-settings,item:c2.tex] -Bookmarks= +Bookmarks=319 Encoding=UTF-8 FoldedColumns= FoldedLines= @@ -112,40 +112,40 @@ ReadWrite=true [item:bibliography.bib] archive=true -column=0 +column=61 encoding=UTF-8 highlight=BibTeX -line=65 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