\"The importance of metal forming by extrusion was reviewed. A Finite Element Approach was developed to analyze extrusion processes. A brick type linear element and the Upper Bound theorem were used to analyze the extrusion of a cylindrical billet into a square cross-section prism. A minimization technique for a non-linear functional with linear constraints was developed. Different types of boundary conditions were also formulated. A frictionless extrusion was simulated using the computer program developed. Velocity profiles at different sections of the deforming solid were obtained and an average extrusion pressure was predicted for a given area reduction ratio.
Extrusions from a cylindrical billet into a square cross-section prism were performed for four different area reduction ratios: 1:2.26, 1:2.55, 1:2.97 and 1:3.34. A Beta Press manufactured by Pressure Technology Corporation of America was used. Billets were made from 6061 T 651 Aluminium.
The effect of friction was investigated analytically. Also a brick type quadratic element (20 nodes) was tested successfully using the compression of a short cylinder as an example\"--Abstract, page iii.
","abstract_html":"<p>"The importance of metal forming by extrusion was reviewed. A Finite Element Approach was developed to analyze extrusion processes. A brick type linear element and the Upper Bound theorem were used to analyze the extrusion of a cylindrical billet into a square cross-section prism. A minimization technique for a non-linear functional with linear constraints was developed. Different types of boundary conditions were also formulated. A frictionless extrusion was simulated using the computer program developed. Velocity profiles at different sections of the deforming solid were obtained and an average extrusion pressure was predicted for a given area reduction ratio.</p> <p>Extrusions from a cylindrical billet into a square cross-section prism were performed for four different area reduction ratios: 1:2.26, 1:2.55, 1:2.97 and 1:3.34. A Beta Press manufactured by Pressure Technology Corporation of America was used. Billets were made from 6061 T 651 Aluminium.</p> <p>The effect of friction was investigated analytically. Also a brick type quadratic element (20 nodes) was tested successfully using the compression of a short cylinder as an example"--Abstract, page iii.</p>","abstract_has_math":false,"creators":["Phu, Nguyen Don"],"institution":"University of Missouri--Rolla","degree_name":"Ph. D. in Mechanical Engineering","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:19:38Z","subjects":["Mechanical Engineering"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/287","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Phu, Nguyen Don"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Mechanical Engineering"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Missouri--Rolla"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mechanical Engineering"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/287"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["\"The importance of metal forming by extrusion was reviewed. A Finite Element Approach was developed to analyze extrusion processes. A brick type linear element and the Upper Bound theorem were used to analyze the extrusion of a cylindrical billet into a square cross-section prism. A minimization technique for a non-linear functional with linear constraints was developed. Different types of boundary conditions were also formulated. A frictionless extrusion was simulated using the computer program developed. Velocity profiles at different sections of the deforming solid were obtained and an average extrusion pressure was predicted for a given area reduction ratio.
Extrusions from a cylindrical billet into a square cross-section prism were performed for four different area reduction ratios: 1:2.26, 1:2.55, 1:2.97 and 1:3.34. A Beta Press manufactured by Pressure Technology Corporation of America was used. Billets were made from 6061 T 651 Aluminium.
The effect of friction was investigated analytically. Also a brick type quadratic element (20 nodes) was tested successfully using the compression of a short cylinder as an example\"--Abstract, page iii.
"]},{"key":"dc:title","label":"Title","values":["A finite element method for three-dimensional analysis of metal forming"]}]}],"canonical_facts":{"dc:creator":["Phu, Nguyen Don"],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["\"The importance of metal forming by extrusion was reviewed. A Finite Element Approach was developed to analyze extrusion processes. A brick type linear element and the Upper Bound theorem were used to analyze the extrusion of a cylindrical billet into a square cross-section prism. A minimization technique for a non-linear functional with linear constraints was developed. Different types of boundary conditions were also formulated. A frictionless extrusion was simulated using the computer program developed. Velocity profiles at different sections of the deforming solid were obtained and an average extrusion pressure was predicted for a given area reduction ratio.
Extrusions from a cylindrical billet into a square cross-section prism were performed for four different area reduction ratios: 1:2.26, 1:2.55, 1:2.97 and 1:3.34. A Beta Press manufactured by Pressure Technology Corporation of America was used. Billets were made from 6061 T 651 Aluminium.
The effect of friction was investigated analytically. Also a brick type quadratic element (20 nodes) was tested successfully using the compression of a short cylinder as an example\"--Abstract, page iii.
"],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/287"],"dc:subject":["Mechanical Engineering"],"dc:title":["A finite element method for three-dimensional analysis of metal forming"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Mechanical Engineering"],"thesis:institution_name":["University of Missouri--Rolla"]},"updated_at":"2026-07-24T03:19:38Z"}