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Shape optimization is widely used, but it typically changes only the mid-surface while keeping topology fixed; topology optimization can add cut-outs, yet then fixes the mid-surface. No method integrates the deep drawing process as manufacturing simulation directly into the optimization. A new topology optimization approach jointly optimizes mid-surface design and cut-outs by combining nonlinear deep-drawing simulation with topology optimization based on linear finite element calculations.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/topology-and-shape-optimization-of-sheet-metals-with-integrated-deep-drawing-simulation/664165/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/topology-and-shape-optimization-of-sheet-metals-with-integrated-deep-drawing-simulation/664165.png","ImageObject",300,407,{"name":92,"@type":93},"OKfine","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-29",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What limitation do traditional shape and topology optimization methods have for deep-drawn sheet metals?","Question",{"text":112,"@type":113},"Shape optimization usually modifies the mid-surface while keeping topology fixed, while topology optimization with cut-outs often fixes the mid-surface as well. Neither approach accounts for the deep drawing process as manufacturing simulation within the optimization loop.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the proposed approach integrate deep drawing simulation into topology optimization?",{"text":117,"@type":113},"It implements nonlinear deep-drawing simulation within a topology optimization framework that uses linear finite element calculations for the optimization step. Deep drawing results are then used to guide local smoothing to manage critical locations.",{"name":119,"@type":110,"acceptedAnswer":120},"How is tearing risk addressed in the optimization workflow?",{"text":121,"@type":113},"The method checks whether tearing is likely to occur during deep drawing. Based on the simulation outcomes, the sheet-metal structure is locally smoothed at critical locations to avoid tearing, while keeping process parameters constant.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},664165,1793242163,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962093957596,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","TOPOLOGY AND SHAPE OPTIMIZATION OF SHEET METALS WITH INTEGRATED DEEP-DRAWING-SIMULATION  \nROBERT DIENEMANN 1, AXEL SCHUMACHER1 AND SIERK FIEBIG2  \n1 University of Wuppertal, School of Mechanical and Safety Engineering, Chair of Optimization of Mechanical Structures, Gaußstraße 20, 42119 Wuppertal, Germany e-mail: [dienemann@uni-wuppertal.de](dienemann@uni-wuppertal.de), [schumacher@uni-wuppertal.de](schumacher@uni-wuppertal.de)  \n2 Volkswagen AG, Gifhorner Straße 180, 38037 Braunschweig e-mail: [sierk.fiebig@volkswagen.de](sierk.fiebig@volkswagen.de)  \nKeywords: Topology optimization, Sheet Metals, Deep Drawing, Manufacturing Simulation, Manufacturing Constraint.  \nAbstract. Shell structures manufactured by deep drawing are important components of lightweight designs for industrial purposes. Shape optimization is excessively used in order to improve the shells performance. Thereby the mid surface design can be changed, but the topology is fixed. Topology optimization can be used to introduce cut-outs into shell structures, but then the mid surface design is fixed. Furthermore there has been no attempt to consider the deep drawing process as manufacturing simulation in the optimization process.  \nIn order to optimize the mid surface design and cut-outs simultaneously, a new topology optimization approach for shell structures has been developed [1]. The current paper focusses on the implementation of the nonlinear deep drawing simulation to the topology optimization based on linear finite element calculations. It is checked if tearing is likely occur during the deep drawing process and according to the deep drawing results, the sheet meal structure is smoothed locally at critical locations to avoid the tearing.  \n1 INTRODUCTION  \nTopology optimization is already widely used in order to get ideas for lightweight constructions. Without manufacturing constraints the topology optimization results can usually only be manufactured by 3Dprinting because of the neglect of the manufacturing process and the complex resulting geometries with an arbitrary change of the cross sections and undercuts.  \nFor several production processes some geometrical requirements on the final design can be handled during the topology optimization. For example casting parts should not have undercuts in the direction of demolding and a draft angle. Sheet metals manufactured by deep drawing should have a constant wall thickness and no undercuts in punch direction [1] .  \nBut fulfilling these geometrical requirements are not sufficient to guarantee a successful manufacturing. The casting mold can possibly not be completely filled or solidifies with porosities or shrinking defects. The deep drawing of sheet metals can possibly initiate cracks (tearing) in the blank (e.g. at low corner radii) or result in wrinkling (e.g. because of low blank holder force) .  \nThis paper focuses on the prevention of tearing at low corner radii during the topology optimization of deep drawn sheet metals. This defect is caused by the geometry of the sheet metal and can therefore be prevented by a slight modification of the structure. The process parameter (blank holder force, friction etc.) are considered as being constant and no design variables. This parameter of the deep drawing process can be used as tuning factors to prevent other defects by maintaining the blank’s geometry.  \n2 TOPOLOGY OPTIMIZATION APPROACH  \nAs topology optimization algorithm the artificial element densities are updated gradient based using the SIMP approach [2] [3]  \nEi = xi sE0 xi ∈]0, 1], (1)  \nwhere xi are the artificial element densities with xi≈0 representing void and xi≈ 1 representing solid material. Ei is the Young’s Modulus of element i and E0 is the Young’s Modulus of the solid material. An increasing penalty exponent s > 1 results in a lower stiffness of intermediate density elements. The design space is discretized with 8-node trilinear finite elements in a structured grid (voxel elements) .  \nTh","cbCaisn1b0Haz6IU","https://ap.wps.com/l/cbCaisn1b0Haz6IU","pdf",2511944,11,"English","# Introduction\n# Topology Optimization Approach","[{\"question\":\"What limitation do traditional shape and topology optimization methods have for deep-drawn sheet metals?\",\"answer\":\"Shape optimization usually modifies the mid-surface while keeping topology fixed, while topology optimization with cut-outs often fixes the mid-surface as well. Neither approach accounts for the deep drawing process as manufacturing simulation within the optimization loop.\"},{\"question\":\"How does the proposed approach integrate deep drawing simulation into topology optimization?\",\"answer\":\"It implements nonlinear deep-drawing simulation within a topology optimization framework that uses linear finite element calculations for the optimization step. Deep drawing results are then used to guide local smoothing to manage critical locations.\"},{\"question\":\"How is tearing risk addressed in the optimization workflow?\",\"answer\":\"The method checks whether tearing is likely to occur during deep drawing. Based on the simulation outcomes, the sheet-metal structure is locally smoothed at critical locations to avoid tearing, while keeping process parameters constant.\"}]","TOPOLOGY AND SHAPE OPTIMIZATION OF SHEET METALS WITH INTEGRATED DEEP-DRAWING-SIMULATION | PDF",28]