Avaliação de erro no cálculo do volume de sólidos irregulares

• Autor(a) principal: Alizeibek Saleimen Nader
• Data de Publicação: 2004
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/BUOS-8DNFGU
• topic: 3D; Métodos numéricos; Modelagem geológica por computador; Tridimensional; Sólidos; Engenharia metalúrgica

This masters dissertation presents in greater level of details two of the most used methods for performing volume calculation for irregular solids: the blocks and subblocks method and the vector integration method. It starts by discussing forms for the analytical calculation of volumes, presents its deficiencies for treating irregular solids and proposes the use of numerical methods. Separately these methods are studied and their theoretical background is presented in a complete manner denoting their similarities and differences. Visual examples ofirregular bi-dimensional regions are discussed in the light of stability and behaviour of the volumetric errors in situations of translation, convexity and non-convexity. Subsequently, area calculations are performed using the two distinct methods, in regions represented by pre-determined functions whose analytical values are known. The vector and blocks pattern is visually presented and the analytical calculation for these areas is demonstrated. The new concept of gaussian vector integration is introduced where the technology of vector integration is enhanced by the Gauss quadrature technique. Detailed descriptions about the gaussian technique and about the conjunction of the two methods are presented.Comparative studies of the methods using regular solids (cylinder and cone) and irregular solids are executed. One of the irregular solids was created step by step by the difference of known regular solids. Computer software available in the market was used to perform the calculation for each of the methods and the error and time of execution was measured for each case. Graphics and tables with the results that were obtained are presented. A brief discussion concerning the importance of the basic information available in real cases is made followed by the conclusions and final comments. A very brief comment is provided on new promising emerging technologies for the calculation of volumes of irregular solids.The on going development of mathematical algorithms and computer technology will make these technological advances available for products suitable to the mineral industry.