\nIntroduction:
\nThe objective of this report is to discuss the effects the linear and non-linear tension
\nhas on the analytical model of a cube.
\nFor the first problem, it was required to sketch a cube of specific dimensions. The
\ncube was assigned specific materials of young modulus of E=110 Mpa and Poisson
\nratio of v=0.35
\nThe cube was then assigned linear and non-linear tension modes and the results
\ncompared for both cases.
\nFinite element results from Abaqus:
\nIn fig.1, a contour plot of the displacement along the x-axis is present for both linear
\nand non-linear tension cubes.
\nDiscussion:
\nIn a linear element the displacement across the element is considered linear. In
\nother words, you can use simple interpolation between nodes to find the
\ndisplacement at any point on a linear element.
\nNon-linear here means that the curve load-displacement is no more proportional.
\nAs\tseen\tin\ttable\t1\tabove:
\n– For\tLinear\tGeometry:\tThe\tNominal\tstain,\tnominal\tstress\tand\tforce\tper\tnodes\tare\t
\napproximately\tequal\tin\tboth\tcases\tfor\tthe\tabaqus\tand\ttheoretical\tresults.
\n– For\tNon-Linear\tGeometry:\tThe\ttrue\tstrain,\tstrain\talong\ty-axis\tand true\tstress\tare\t
\napproximately\tequal\tin\tboth\tcases\tfor\tthe\tabaqus\tand\ttheoretical\tresults.
\n– The\tnodal\tforce\tfor\tthe\tnon-linear\tgeometry\tis\tnon\taccurate\twhen\tcomparing\tthe\t
\nabacus\tresults\tand\ttheoretical\tresults.
\nTable\t1,\tdemonstrates\tthe\teffect\tthe\tNLGEOM\tmode\thas\ton\tan\tanalytical\tmodel\tof\ta\t
\ncube\tunder\tspecific\tboundary\tconditions.
\nFurthermore,\tthe\ttwo\tplots\tin\tfig4\t&\tfig5\tfurther\tdemonstrates\tthe\tdifferences\tin\tresults\tthe\t
\nNLGEOM\tmode\thas\ton\tresults.\tIt\talso\tshows\tthat\tfor\tthe\tgeometric\tnon\tlinearity,\tthe\tstrain\t
\nvaries\tas\twell\tas\tthe\tdisplacement\tas\tthe\tapplication\tof\tthe\tload\tbecomes\tnon\tuniform.
\nProblem\t2
\nIntroduction:
\nIn\tproblem\t2,\ta\tpoint\tload\tof\t1.3933\tmm\twas\tapplied\tto\tthe\tcorner\tof\ta\tcube.\tFor\tcase\t1,\tthe\t
\ncube\twas\tmeshed\twith\telement\ttype\tC3D8,\twhich\tis\ta\tfull\tintegration\thexahedral\telement.\t
\nFor\tthe\tsecond\tcase,\tVon\t-Mises\tresults\tare\tcompared\tfor\tboth\tcases.
\nDiscussion:
\nThe maximum stress with element type C3D8 is almost four times greater than the
\nmaximum stress with element type C3D8
\nThis highlights the important of choosing the right element type to mesh the design,
\nas it has a large impact on the Von-misses (deformation) results and analysis.
\nHourglass term come into picture if you are using reduced integration elements.
\nBecause of under integration you will get spurious modes, which needs to be
\navoided as it produces meaningless results.
\nDue to the complexity of distribution of the point stress on the cube corner, the
\ndesign required an element type to be analysed accurately by using fully integrated
\nelements not reduced integration.
\nAs seen in fig.6, there is almost an error in the formation representation given
\nassigning as an element type to the mesh.
\nThe results above in fig.6 verify that Hourgalssing can be addressed by using fully
\nintegrated elements.
\nProblem\t3
\nIntroduction:
\nIn\tproblem\t3,\tthe\ttask\tis\tto\thighlight\tthe\tdifferences\tand\tlimitation\tbetween\tthe\telement\t
\nchoices\ton\tAbacus.\tThe\tfollowing\tthree\telements\twill\tbe\tcompared\tto\tthe\ttheoretical\t
\nresults:
\n? Reduced\tintegration\thexahedral\t(brick)\telement\t(C3D8R)
\n? Full\tintegration\tlinear\thexahedral\t(brick)\telement(C3D8)
\n? Incompatible\telement\t(C3D8I)
\nA\tconcentrated\tforce\twill\tbe\tapplied\twith\tmagnitude\tof\t8000N\tto\tthe\tvertices\tof\ta\tset\tof\t
\npoint
\nThe\tforce\twill\tresults\tin\tthe\tdownward\tbending\tof\tthe\tbeam\tand\ta\tstep\twill\tbe\tcreated\tfor\t
\nanalysis\tof\tat\tleast\t20\tincriminations.
\nThe\tresults\tfrom\tthe\t3\tsimulations\twill\tbe\tpresented\talong\twith\tplots\tof\tthe\tshape\tof\tthe\t
\ndeformed\tbeam.
\nLastly,\tthere\twill\tbe\ta\tbrief\tdiscussion\tof\tresults\tand\tcomparisons\twith\ttheoretical\t
\ncalculation.
\nDiscussion:
\nThe\t reduced\tintegration\t results\t for\t deflection\t compared\t to\t the\t theoretical\t calculation\tare\t
\noff\t by\t a\t margin\t of\t about\t 10\t mm\t which\t is\t very\t inaccurate\t and\t proves\t that\t the\t reduced\t
\nintegration\tis\tnot\taccurate\tand\ta\tbad\tchoice\tfor\ttrying\tto\tpredict\tthe\tbending\tresponse\tof\ta\t
\nbeam.
\nOn\t the\t other\t hand\t the\t full\tand\t incompatible\t integration\t seem\t to\t be\t quite\taccurate\twhen\t
\ncompared\t to\t the\t theoretical\t results\t in\t fig.\t and\t table.\t 2and\t fig.8\t .This\t proves\t that\t full\t and\t
\nincompatible\tintegration\tare\tboth\tgood\tchoices\tfor\tpredicting\tthe\tbeams\tbending\tresponse\t
\nand\tdeflection\talong\tthe\tdeformed\tbeam.
\nHowever\tin\tfig.7,\tthere\tis\tan\tinaccuracy\tin\tthe\tstress\tvalues\tfor\tthe\tfull\tintegration\telements.\t
\nTherefore,\t the\t incompatible\t integration\t would\t be\t more\t accurate\t in\t interpreting\t accurate\t
\noverall\t results\t for\t the\t deflection\t of\t the\t beam.\t As\t it\t couses\t enhancements\t to\t the\t
\ndeformation\t gradients\t which\t allow\t a\t first-order\t element\t to\t have\t a\t linear\t variation\t of\t the\t
\ndeformation\tgradient\tacross\tthe\telement’s\tdomain.
\nTo\tconclude,\telement\tchoices\thave\tproven\tto\thave\ta\tmissive\timpact\ton\tthe\tresults\tobtained\t
\nform\tabacus.\tChoosing\tthe\tright\telement\ttype\tis\tcrucial\twhen\tanalysis\ta\tdesign\ton\tabacus,\tas\t
\nthe\tintegrity\tof\tthe\tresults\tmight\tbe\teffected\tand\timpact\tgreatly\ton\tthe\tperformance\tof\tthe\t
\ndesigned\tmodel.<\/p>\n","protected":false},"excerpt":{"rendered":"
Introduction: The objective of this report is to discuss the effects the linear and non-linear tension has on the analytical model of a cube. For the first problem, it was required to sketch a cube of specific dimensions. The cube Read More …<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-6982","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/6982","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=6982"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/6982\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=6982"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=6982"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=6982"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}