The desire to follow student learning within intelligent tutoring systems in near real time has led to the development of several models anticipating the correctness of the next item as students work through an assignment. Such models have in- cluded Bayesian Knowledge Tracing (BKT), Performance Factors Analysis (PFA), and more recently with developments in Deep Learning, Deep Knowledge Tracing (DKT). The DKT model, based on the use of a recurrent neural network, exhibited promising results in paper [PBH+15]. Thus far, however, the model has only considered the knowledge components of the problems and correctness as input, neglecting the breadth of other features col- lected by computer-based learning platforms. This work seeks to improve upon the DKT model by incorporating more features at the problem-level and student-level. With this higher dimensional input, an adaption to the original DKT model struc- ture is also proposed, incorporating an Autoencoder network layer to convert the input into a low dimensional feature vector to reduce both the resource requirement and time needed to train. Experimental results show that our adapted DKT model, which includes more combinations of features, can effectively improve accuracy.

Neste trabalho apresenta-se um elemento finito de casca plano que é obtido pela composição de um elemento de placa com um de membrana. O elemento de placa usado, o DKT (Discrete Kirchhoff Theory), pertence à classe dos elementos triangulares com nove graus de liberdade (uma translação e duas rotações por nó), e é obtido pela imposição da hipótese de Kirchhoff nos seus pontos nodais. Para o elemento de membrana, usou-se o elemento CST (Constant Strain Triangle), com seis graus de liberdade (duas translações por nó). O elemento finito resultante DCT, possui dezoito graus de liberdade (três translações e três rotações, sendo uma das rotações fictícia- no plano do elemento). Simples exemplos de placa e chapa no espaço foram analisados para se testar o elemento, e finalmente uma casca cilíndrica uniformemente carregada foi analisada e o resultado obtido comparado com o fornecido por outros autores. Neste estudo, o elemento DKT mostrou-se eficiente na análise de cascas. / This work presents a flat shell finite element composed of plates in bending and in tension finite elements. The bending element used, the DKT (Discrete Kirchhoff Theory) belongs to the class of triangular elements with nine degrees of freedom (the transverse displacement and its derivatives at each node) and it is obtained from the theory of plates with shear force influence with Kirchhoff hypothesis imposed in the nodes of the element. The tension finite element is the well known CST (Constant Strain Triangle) with six degrees of freedom (the displacement u and v at each node). The resulting finite element, called DCT, has 18 degrees of freedom, including an extra and fictitious rotation in the normal direction to the surface of elements. Single plates in bending and in tension described in a tridimensional system of coordinates were analyzed to test the adopted finite elements and finally cylindrical shell uniformly loaded were analyzed and the results compared with those of authors. In the work the DKT element shown to be a reliable finite element to be used in shell analysis.

Neste trabalho apresenta-se um elemento finito de casca plano que é obtido pela composição de um elemento de placa com um de membrana. O elemento de placa usado, o DKT (Discrete Kirchhoff Theory), pertence à classe dos elementos triangulares com nove graus de liberdade (uma translação e duas rotações por nó), e é obtido pela imposição da hipótese de Kirchhoff nos seus pontos nodais. Para o elemento de membrana, usou-se o elemento CST (Constant Strain Triangle), com seis graus de liberdade (duas translações por nó). O elemento finito resultante DCT, possui dezoito graus de liberdade (três translações e três rotações, sendo uma das rotações fictícia- no plano do elemento). Simples exemplos de placa e chapa no espaço foram analisados para se testar o elemento, e finalmente uma casca cilíndrica uniformemente carregada foi analisada e o resultado obtido comparado com o fornecido por outros autores. Neste estudo, o elemento DKT mostrou-se eficiente na análise de cascas. / This work presents a flat shell finite element composed of plates in bending and in tension finite elements. The bending element used, the DKT (Discrete Kirchhoff Theory) belongs to the class of triangular elements with nine degrees of freedom (the transverse displacement and its derivatives at each node) and it is obtained from the theory of plates with shear force influence with Kirchhoff hypothesis imposed in the nodes of the element. The tension finite element is the well known CST (Constant Strain Triangle) with six degrees of freedom (the displacement u and v at each node). The resulting finite element, called DCT, has 18 degrees of freedom, including an extra and fictitious rotation in the normal direction to the surface of elements. Single plates in bending and in tension described in a tridimensional system of coordinates were analyzed to test the adopted finite elements and finally cylindrical shell uniformly loaded were analyzed and the results compared with those of authors. In the work the DKT element shown to be a reliable finite element to be used in shell analysis.