Hi
I want to model a composite laminate by shell99 in ANSYS.This laminate is symmetrical about the midplane,so I adjust Layer Symmetry Key(LSYM) to 1 and halve the number of layers. when I compare the maximum deflection of this model with the max deflection of the model with LSYM=0(by inputing total layers) there is a big difference between these two results. It's natural that the results should be the same. I don't know why this error occurs.
I'm teaching Applied Mathematics 105a this semester. The main content of the course is complex analysis. The course is taken mainly by undergraduate students in Engineering, Physics, and Applied Mathematics. There are about 70 people in the class, which makes it the largest class I have taught in the last 10 years. I have never taught a course on complex analysis before, but have used complex analysis in my research, and have taught the method of complex variables in my graduate course on elasticity.
The Lemaitre damage material model was developed by Lemaitre for an isotropic linear elastic virgin material with stress-strain law as follows
\begin{equation}
\label{eq:22}
\sigma_{ij}=(1-D)C_{ijkl}\epsilon_{kl} \quad D\in[0,1]
\end{equation}
where $D$ represents the extent of damage with the damage evolution law
\begin{equation}
\label{eq:23}
D(\bar{\epsilon})=1-(1-A)\epsilon_{D_{0}}\bar{\epsilon}^{-1}-Ae^{-B(\bar{\epsilon}-\epsilon_{D_{0}})}
\end{equation}
H. Mei, Y. Pang, and R. Huang, International Journal of Fracture 148, 331-342 (2007).
Following a previous effort published in MRS Proceedings, we wrote a journal article of the same title, with more numerical results. While the main conclusions stay the same, a few subtle points are noted in this paper.
Lei and I will be working on developing the appropriate relations and numerical methods for topological optimization of 2D ideal structures. In this constraint-based optimization study we will try to determine the density distribution which minimizes the strain energy for a fixed volume of material. This problem is a subset of the so-called "G-closure" problem in topological optimization where we have restricted our possible configurations to certain ideal geometries.
Andrew and I decided to work on some design topics.
Given a reference domain, some boundary conditions and a limited amount of material, which can not fill the whole domain, we want to determine the material distribution inside the domain so that the structure generated will contain the minimum elastic energy. This is called minimum compliance problem, a topic in the field of topology optimization.
Nathan Thielen and I will be investigating straight beams, bent beams and how the analysis can be applied to hooks. We did not have much time to investigate beams in ES240 this term so we hope to gain a broader understanding of this area and share our findings with the rest of the class. The primary goal is to compare the analysis necessary for straight beams versus the analysis needed for bent beams. We choose the project because we also will have ample opportunity to investigate bent beams and hooks using FEM.
Hi everyone,
Christian and I thought comparing the theory of bent beams to that of straight beams would be interesting because we only explored straight beams this semester in class. Bent beams are important since they are encountered regularly in practice, for example a hook. The geometry of a bent beam changes the equations governing the behavior. So, understanding how the geometry changes the beams behavior is our primary interest.
