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[416], 'co-ordinate': [417], 'systems.': [418], 'An': [419, 1648], 'killing': [421], 'strategy': [422], 'presented': [424], 'reduce': [426], 'total': [428], 'number': [429], 'degrees': [431], 'freedom': [433], 'improve': [435], 'computational': [437, 573, 1346], 'efficiency.': [438], 'simple': [440, 802], 'constraint': [441], 'handling': [442], 'approach': [443, 546, 553, 582, 1973], 'proposed': [445, 474], 'minimum': [448, 536], 'compliance': [449, 537, 832], 'volume': [453], 'constraint.': [454], 'physically': [456], 'meaningful': [457], 'numerically': [459], 'velocity': [461], 'extension': [462], 'avoid': [467], 'complicated': [469], 'PDE': [470], 'solving': [471], 'procedure.': [472], 'applied': [478], 'effective': [490], 'elasticity': [499, 506], 'problems.': [502], 'For': [503, 534], 'classical': [505], 'problems': [507, 540, 1015, 1229, 1274], 'literature,': [510], 'present': [512, 545, 581, 597], 'can': [514, 599], 'achieve': [515], 'results': [517, 529], 'good': [519], 'agreement': [520], 'those': [522], 'theoretical': [525, 590], 'solutions': [526], 'and/or': [527], 'standard': [532], 'FEM.': [533], 'optimization,': [543], 'significantly': [547], 'outperforms': [548], 'well-recognized': [550], "'ersatz": [551], "material'": [552], 'expected': [555], 'accuracy': [558], 'strain': [561], 'field,': [562], 'stability,': [564], 'representation': [566], 'fidelity': [567], 'at': [568], 'expense': [570], 'increased': [572], 'time.': [574], 'It': [575, 592], 'also': [577], 'shown': [578], 'that': [579, 595], 'able': [584], 'produce': [586], 'structures': [587], 'near': [588], 'optimum.': [591], 'suggested': [594], 'be': [600], 'promising': [602], 'methods.': [613, 861, 1081, 1745, 1783, 1922], 'Copyright': [614], '©': [615], 'John': [617], '&': [619], 'Sons,': [620], 'Ltd.': [621], 'REFERENCES': [622], '1': [623], 'Michell': [624], 'AGM.': [625], 'limits': [627], 'economy': [629], 'material': [631, 788], 'frame-structures.': [633], 'Philosophical': [634], 'Magazine': [635], '1904;': [636], '8(6):': [637], '589–597.': [638], '2': [639], 'Bendsøe': [640, 781, 1148, 1602], 'MP,': [641, 1603], 'Kikuchi': [642, 1429], 'N.': [643, 1455], 'Generating': [644], 'optimal': [645, 1762], 'topologies': [646], 'homogenization': [652], 'method.': [653, 884, 1202, 1253, 1384, 1953, 2021], 'Computer': [654, 907, 934, 1203, 1235, 1278, 1466, 1525, 1631, 1678, 1849, 1928], 'Applied': [657, 910, 1206, 1238, 1281, 1308, 1634, 1681, 1787], 'Mechanics': [658, 911, 1058, 1207, 1239, 1282, 1635, 1682], 'Engineering': [660, 913, 937, 963, 1088, 1112, 1163, 1187, 1209, 1241, 1284, 1334, 1420, 1440, 1469, 1498, 1551, 1637, 1662, 1684, 1705], '1988;': [661, 987], '71:': [662], '197–224.': [663], '3': [664], 'Rozvany': [665, 764, 827], 'GIN.': [666, 828], 'Aims,': [667], 'scope,': [668], 'history': [670], 'unified': [672], 'terminology': [673], 'computer-aided': [675], 'mechanics.': [680], 'Structural': [681, 695, 756, 775, 791, 820, 840, 852, 876, 1620], 'Multidisciplinary': [683, 758, 842], 'Optimization': [684, 735, 759, 776, 792, 843], '2001;': [685, 728, 760, 844, 1030, 1113, 1210, 1685, 1825, 1872], '21(2):': [686, 761], '90–108.': [687], '4': [688], 'Hassani': [689], 'B,': [690, 1736, 1940, 1967], 'Hinton': [691, 710], 'E.': [692, 711], 'Homogenization': [693, 738], 'Topology': [696, 950, 1606, 1671], 'Optimization:': [697, 1607, 1717], 'Theory,': [698, 1608], 'Practice': [699], 'Software.': [701], 'Springer:': [702, 740, 822, 1002, 1612, 1728], 'London,': [703, 823], '1999.': [704, 1799], '5': [705], 'Bulman': [706], 'S,': [707, 969, 1008, 1098, 1292, 1366, 1428, 1806, 1856, 1877, 1942], 'Sienz': [708], 'J,': [709, 1143, 1264, 1290, 1316, 1711], 'Comparisons': [712], 'between': [713], 'algorithms': [714, 978, 1626], 'series': [721], 'benchmark': [723], 'studies.': [724], 'Computers': [725, 808, 1254], 'Structures': [727, 810, 1138, 1256], '79(12):': [729], '1203–1218.': [730], '6': [731], 'Allaire': [732, 870], 'G.': [733], 'Shape': [734, 1716, 1718], 'Method.': [739], 'New': [741, 1003, 2005], 'York,': [742, 1004, 2006], '2001.': [743], '7': [744], 'Sigmund': [745, 1604], 'O.': [746, 1605], '99': [748], 'line': [749], 'code': [752], 'written': [753], 'MATLAB.': [755], '120–127.': [762], '8': [763], 'GIN,': [765], 'Zhou': [766], 'M,': [767, 1342, 1734], 'Birker': [768], 'T.': [769, 1171, 1404], 'Generalized': [770, 1220], 'without': [773], 'homogenization.': [774], '1992;': [777, 1257], '4:': [778], '250–254.': [779], '9': [780], 'MP.': [782, 1149], 'Optimal': [783], 'distribution': [789], 'problem.': [790], '1989;': [793], '1:': [794], '193–202.': [795], '10': [796], 'Xie': [797, 815], 'YM,': [798, 816], 'Steven': [799, 817], 'GP.': [800, 818], 'evolutionary': [803], 'procedure': [804], 'optimization.': [807, 906, 933, 1156, 1655, 1698], '1993;': [811], '49(5):': [812], '885–896.': [813], 'Evolutionary': [819], 'Optimization.': [821], 'UK,': [824, 1798], '1997.': [825, 1071], '12': [826], 'Stress': [829, 1995], 'ratio': [830], 'based': [833, 979, 1040, 1814], 'optimization—a': [837], 'critical': [838], 'review.': [839], '21:': [845, 1912], '109–119.': [846], '13': [847], 'Sethian': [848, 970, 1775], 'JA,': [849], 'Wiegmann': [850], 'A.': [851, 1266], 'via': [855], 'immersed': [859], 'interface': [860], 'Computational': [864, 887, 985, 1028, 1724, 1748, 1789, 1870, 1956, 1985], 'Physics': [865, 888, 986, 1029, 1749, 1871, 1957, 1986], '2000;': [866, 1361, 1911], '163(2):': [867], '489–528.': [868], '14': [869], 'G,': [871, 1402], 'Jouve': [872], 'F,': [873], 'Toader': [874], 'AM.': [875], 'sensitivity': [879, 926], 'level-set': [883, 1039, 1837], '2004;': [889, 940, 1164, 1421, 1442, 1472, 1552, 1750], '194:': [890, 1751], '363–393.': [891], '15': [892], 'MY,': [894, 919, 1035, 1645, 1690], 'X,': [896, 1576], 'Guo': [897], 'D.': [898, 1899], '2003;': [914, 964, 1242, 1391, 1499, 1598], '192:': [915, 1243], '227–246.': [916], '16': [917], 'X.': [921, 1037], 'PDE-driven': [922], 'sets,': [924], 'curvature': [928, 975], 'flow': [929], 'Modeling': [935, 1467], 'Sciences': [939, 1471], '6(4):': [941, 1473], '373–395.': [942], '17': [943], 'Belytschko': [944, 1073, 1093, 1168, 1261, 1403], 'T,': [945, 1074, 1094, 1169, 1193, 1215, 1262, 1451, 1668, 1965], 'Xiao': [946], 'SP,': [947], 'Parimi': [948, 1099], 'C.': [949, 1100], 'functions': [954], 'regularization.': [956], '57(8):': [965], '1177–1196.': [966], '18': [967], 'Osher': [968, 991, 1007, 1855, 1876, 1941, 1968], 'JA.': [971, 1776], 'Front': [972], 'propagating': [973], 'dependent': [976], 'speed:': [977], 'on': [980, 1270, 1588, 1758, 1786, 1889, 1908, 2024], 'Hamilton–Jacobi': [981, 1885, 1904], 'formulations.': [982], '78:': [988], '12–49.': [989], '19': [990], 'SJ,': [992], 'Fedkiw': [993, 1857, 1962], 'RP.': [994, 1858], 'Set': [996], 'Dynamic': [999, 1565], 'Implicit': [1000], 'Surfaces.': [1001], '2002.': [1005], '20': [1006], 'Santosa': [1009], 'F.': [1010], 'Level-set': [1011], 'involving': [1016], 'geometry': [1017, 1151], 'constraints:': [1019], 'frequencies': [1020], 'two-density': [1023], 'inhomogeneous': [1024], 'drum.': [1025], '171:': [1031], '272–288.': [1032], '21': [1033], 'heterogeneous': [1048], 'objects.': [1049], 'Design': [1051, 1360], '2005;': [1052, 1638, 1706], '37:': [1053, 1090], '321–337.': [1054], '22': [1055], 'Reddy': [1056], 'JN.': [1057], 'Laminated': [1060], 'Composite': [1061], 'Plates:': [1062], 'Theory': [1063], 'Analysis.': [1065, 1568, 1720], 'CRC': [1066], 'Press:': [1067, 1796, 2039], 'Boca': [1068], 'Raton,': [1069], 'FL,': [1070], '23': [1072], 'Lu': [1075], 'YY,': [1076], 'Gu': [1077], 'L.': [1078], 'Element-free': [1079], 'Galerkin': [1080, 1582], '1994;': [1089, 1311], '229–256.': [1091], '24': [1092], 'Moës': [1095], 'N,': [1096, 1340], 'Usui': [1097], 'Arbitrary': [1101, 1478], 'elements.': [1105], '50:': [1114], '993–1013.': [1115], '25': [1116], 'Jang': [1117], 'GW,': [1118], 'Kim': [1119, 1476], 'YY.': [1120], 'Sensitivity': [1121, 1719], 'fixed-grid': [1124], 'oblique': [1129], 'curve': [1131], 'approximation.': [1132], 'Solids': [1136], '2005,': [1139, 1663], 'submitted.': [1140], 'Norato': [1142], 'Haber': [1144], 'R,': [1145, 1294, 1963], 'Tortorelli': [1146], 'D,': [1147, 1370, 1938], 'projection': [1152], '60(14):': [1165], '2289–2312.': [1166], '27': [1167], 'Black': [1170], 'Elastic': [1172], 'crack': [1173], 'growth': [1174], 'minimal': [1179], 'remeshing.': [1180], '1999;': [1188, 1958, 1987], '45(5):': [1189], '601–620.': [1190], '28': [1191], 'Strouboulis': [1192, 1214], 'Copps': [1194], 'K,': [1195, 1368], 'Babuska': [1196, 1218, 2009], 'I.': [1197, 1219], 'generalized': [1199], '190:': [1211, 1686], '4081–4193.': [1212], '29': [1213], 'Zhang': [1216], 'L,': [1217], 'mesh-based': [1225], 'handbooks:': [1226], 'application': [1227], 'domains': [1231], 'many': [1233], 'voids.': [1234], '3109–3161.': [1244], '30': [1245], 'Fish': [1246, 1263, 1289, 1315], 'J.': [1247, 1670, 1713], 's-version': [1249, 1320], '43(3):': [1258], '539–547.': [1259], '31': [1260], 'Bayliss': [1265], 'spectral': [1268, 1583], 'overlay': [1269, 1437, 1464], 'high': [1276], 'gradients.': [1277], '1990;': [1285], '81:': [1286], '71–89.': [1287], '32': [1288], 'Markolefas': [1291], 'Guttal': [1293, 1317], 'Nayak': [1295], 'P.': [1296, 1834], 'On': [1297, 1431], 'adaptive': [1298], 'multilevel': [1299], 'superposition': [1300], 'meshes': [1304, 1482], 'elastostatics.': [1307], 'Mathematics': [1310, 1790], '14:': [1312], '135–164.': [1313], '33': [1314], 'R.': [1318], 'laminated': [1326], 'composites.': [1327], '1996;': [1335], '39:': [1336], '3641–3662.': [1337], '34': [1338], 'Takano': [1339], 'Zako': [1341], 'Ishizono': [1343], 'M.': [1344, 1430, 1755, 1946], 'Multi-scale': [1345], 'elastic': [1349], 'bodies': [1350], 'heterogeneity.': [1355], 'Materials': [1359, 1441], '7:': [1362, 1392], '111–132.': [1363], '35': [1364], 'Nakasumi': [1365], 'Suzumi': [1367], 'Fuzii': [1369], 'Ohtsubo': [1371], 'H.': [1372], 'Mixed': [1373], 'shell': [1376], 'solid': [1378], 'Marine': [1387], 'Science': [1388, 1821], 'Technology': [1390, 1823], '180–188.': [1393], '36': [1394], 'Lee': [1395], 'SH,': [1396], 'Song': [1397], 'JH,': [1398], 'Yoon': [1399], 'YC,': [1400], 'Zi': [1401], 'Combined': [1405], 'extended': [1406], 'cracks.': [1413], '59:': [1422], '1119–1136.': [1423], '37': [1424], 'Okada': [1425, 1446], 'H,': [1426, 1447, 1944], 'Endoh': [1427], 'fracture': [1432], 'technique.': [1438, 1465], 'Key': [1439], '261–263:': [1443], '681–686.': [1444], '38': [1445], 'Liu': [1448], 'CT,': [1449], 'Ninomiya': [1450], 'Fukui': [1452], 'Y,': [1453, 1832], 'Kumazara': [1454], 'Analysis': [1456, 1891, 2026], 'particulate': [1458], 'composite': [1459], 'materials': [1460], '333–347.': [1474], '39': [1475], 'HG.': [1477], 'placement': [1479], 'interface-element': [1489], '(IEM).': [1491], '56:': [1500], '2279–2312.': [1501], '40': [1502], 'Kimia': [1503], 'BB,': [1504], 'Tennenbaum': [1505], 'AR,': [1506], 'Zucker': [1507], 'SW.': [1508], 'Shape,': [1509], 'shope': [1510], 'deformations': [1512], 'i:': [1513], 'components': [1515], 'two-dimensional': [1517], 'reaction–diffusion': [1520], 'space.': [1521], 'Vision': [1526, 1850], '1995;': [1527], '15:': [1528], '189–224.': [1529], '41': [1530], 'Zhao': [1531, 1943], 'P,': [1532], 'Heinrichand': [1533], 'JC,': [1534, 1830], 'Poirier': [1535], 'DR.': [1536], 'Fixed': [1537], 'front-tracking': [1539], 'methodology': [1540], 'simulations.': [1544], '61:': [1553], '928–948.': [1554], '42': [1555], 'Hughes': [1556], 'TJR.': [1557], 'Finite': [1559, 1566], 'Element': [1560, 1567], 'Method:': [1561], 'Linear': [1562], 'Static': [1563], 'Dover': [1569], 'Publications:': [1570], 'Mineola,': [1571], 'NY,': [1572], '2000.': [1573], '43': [1574], 'Shi': [1575], 'Lin': [1577], 'JZ,': [1578], 'Yu': [1579], 'ZS.': [1580], 'Discontinuous': [1581], 'lattice': [1585], 'Boltzmann': [1586], 'element.': [1590], 'Fluids': [1597], '42:': [1599], '1249–1261.': [1600], '44': [1601], 'Applications.': [1611], 'Berlin,': [1613, 1729], '2003.': [1614], '45': [1615], 'SY,': [1617, 1643], 'Tai': [1618, 1646], 'K.': [1619, 1647], 'genetic': [1625, 1650], 'bit-array': [1629], 'representation.': [1630], '194(36–38):': [1639], '3749–3770.': [1640], '46': [1641], 'enhanced': [1649], 'algorithm': [1651], 'press.': [1665], '47': [1666], 'Borrvall': [1667], 'Petersson': [1669], 'regularized': [1674], 'intermediate': [1675], 'mass': [1676], 'density.': [1677], '4911–4928.': [1687], '48': [1688], 'SY.': [1692], 'Bilateral': [1693], 'filtering': [1694], '63(13):': [1707], '1911–1938.': [1708], '49': [1709], 'Sokolowski': [1710], 'Zolesio': [1712], 'Introduction': [1714], 'Springer': [1721], 'Series': [1722], 'Mathematics,': [1725], 'vol.': [1726], '10.': [1727], 'Germany,': [1730], '1992.': [1731], '50': [1732], 'Burger': [1733, 1754], 'Hackl': [1735], 'Ring': [1737], 'W.': [1738], 'Incorporating': [1739], 'topological': [1740], 'derivatives': [1741], '344–362.': [1752], '51': [1753], 'Lecture': [1756], 'notes': [1757], 'infinite-dimensional': [1759], 'design.': [1763], 'Report': [1764, 1924], '285J,': [1765], 'California,': [1768], 'Los': [1769], 'Angeles,': [1770], 'CA,': [1771], 'USA,': [1772], '2004.': [1773, 1935], '52': [1774], 'fast': [1781, 1949], 'marching': [1782], 'Cambridge': [1784, 1794], 'Monographs': [1785], '(': [1791, 1998], '2nd': [1792], 'edn).': [1793, 2000], 'Cambridge,': [1797], '53': [1800], 'Richards': [1801], 'DF,': [1802], 'Bloomfield': [1803], 'MO,': [1804], 'Sen': [1805], 'Calea': [1807], 'TS.': [1808], 'Extension': [1809], 'velocities': [1810], 'surface': [1815], 'profile': [1816], 'evolution.': [1817], 'Vacuum': [1820], '19(4):': [1826], '1630–1635.': [1827], '54': [1828], 'Ye': [1829], 'Bresler': [1831], 'Moulin': [1833], 'self-referencing': [1836], 'image': [1840], 'reconstruction': [1841], 'sparse': [1843], 'Fourier': [1844], 'samples.': [1845], '2002;': [1851], '50(3):': [1852], '253–270.': [1853], '55': [1854], 'methods:': [1861], 'overview': [1863], 'some': [1865], 'recent': [1866], 'results.': [1867], '169:': [1873], '463–502.': [1874], '56': [1875], 'Shu': [1878], 'CW.': [1879], 'High-order': [1880], 'essentially': [1881], 'nonoscillatory': [1882], 'schemes': [1883, 1902], 'equations.': [1886, 1905], 'SIAM': [1887, 1906, 2022], '1991;': [1892], '28:': [1893], '907–922.': [1894], '57': [1895], 'Jiang': [1896], 'GS,': [1897], 'Peng': [1898, 1937], 'Weighted': [1900], 'ENO': [1901], 'Scientific': [1909], 'Computing': [1910], '2126–2143.': [1913], '58': [1914], 'Mitchell': [1915], 'IM.': [1916], 'toolbox': [1918], 'Technical': [1923], 'TR-2004-09,': [1925], 'Science,': [1929], 'British': [1932], 'Columbia,': [1933], 'Canada,': [1934], '59': [1936], 'Merriman': [1939, 1966], 'Kang': [1945], 'PDE-based': [1948], '155:': [1959], '410–438.': [1960], '60': [1961], 'Aslam': [1964], 'S.': [1969], 'non-oscillatory': [1971], 'interfaces': [1975], 'multimaterial': [1977], 'flows': [1978], '(the': [1979], 'ghost': [1980], 'fluid': [1981], 'method).': [1982], '152:': [1988], '457–492.': [1989], '61': [1990], 'Roark': [1991], 'RJ.': [1992], 'Formulas': [1993], 'Strain': [1997], '4th': [1999], 'McGraw-Hill': [2001], 'Book': [2002], 'Co.,': [2003], 'Inc.:': [2004], '1965.': [2007], '62': [2008], 'I,': [2010], 'Szabo': [2011], 'BA,': [2012], 'Katz': [2013], 'IN.': [2014], 'p-version': [2016], '1981;': [2027], '18(3):': [2028], '515–545.': [2029], '63': [2030], 'Hemp': [2031], 'WS.': [2032], "Michell's": [2033], 'continua.': [2035], 'Optimum': [2036], 'Structures.': [2037], 'Clarendon': [2038], 'Oxford,': [2040], '1973.': [2041], 'Citing': [2042], 'Literature': [2043], 'Volume65,': [2044], 'Issue1112': [2045], 'March': [2046], '2006Pages': [2047], 'ReferencesRelatedInformation': [2049]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2006796680', 'counts_by_year': [{'year': 2024, 'cited_by_count': 2}, {'year': 2023, 'cited_by_count': 1}, {'year': 2020, 'cited_by_count': 1}, {'year': 2019, 'cited_by_count': 3}, {'year': 2018, 'cited_by_count': 3}, {'year': 2017, 'cited_by_count': 4}, {'year': 2016, 'cited_by_count': 2}, {'year': 2015, 'cited_by_count': 1}, {'year': 2014, 'cited_by_count': 7}, {'year': 2013, 'cited_by_count': 7}, {'year': 2012, 'cited_by_count': 9}], 'updated_date': '2024-09-14T00:30:55.307783', 'created_date': '2016-06-24'}