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'several': [411], 'examples': [412], 'are': [413], 'provided': [414], 'demonstrate': [416], 'effectiveness': [418], 'both': [424], 'problems.': [428, 1098, 1323, 1351, 1409], 'Copyright': [429], '©': [430], 'John': [432], '&': [434], 'Sons,': [435], 'Ltd.': [436], 'References': [437], '1Belytschko': [438], 'T,': [439, 458, 713, 901, 903], 'Lu': [440, 459], 'YY,': [441, 460, 1054], 'Gu': [442, 461], 'L.': [443, 462], 'Element-free': [444], 'Engineering': [453, 469, 520, 540, 563, 640, 660, 687, 708, 734, 761, 783, 810, 830, 877, 896, 919, 946, 995, 1020, 1045, 1122, 1147, 1171, 1215, 1252, 1277, 1300, 1330, 1358, 1414, 1472, 1632], '1994;': [454], '37:': [455], '229–256.': [456], '2Belytschko': [457], 'Crack': [463], 'propagation': [464], 'element-free': [466, 699, 1238], 'Fracture': [470], 'Mechanics': [471, 518, 538, 561, 582, 596, 706, 849, 917, 1018, 1101, 1250, 1328, 1386, 1470, 1496, 1538], '1995;': [472, 492, 618, 1605], '51:': [473], '295–459.': [474], '3Liu': [475], 'WK,': [476, 717, 1455], 'Jun': [477], 'S,': [478, 587, 692, 743, 926, 1257, 1282], 'Zhang': [479, 1051, 1196, 1227, 1306, 1426], 'YF.': [480], 'Reproducing': [481, 503, 1260, 1285], 'Fluids': [491], '20:': [493], '1081–1106.': [494], '4Chen': [495], 'JS,': [496, 739, 788, 924, 977, 1084, 1305, 1337, 1363, 1397, 1419], 'Pan': [497], 'C,': [498], 'Wu': [499, 740, 927, 1364, 1424], 'CT,': [500, 741], 'Liu': [501, 716, 1258, 1283], 'WK.': [502, 1259, 1284], 'Kernel': [504], 'large': [508], 'deformation': [509], 'structures.': [513], 'Computer': [514, 534, 557, 702, 913, 1014, 1246, 1324, 1466, 1602], 'Applied': [517, 537, 560, 705, 916, 1017, 1249, 1327, 1469, 1583], '1996;': [521, 541, 709], '139:': [522, 542, 710], '195–227.': [523], '5Duarte': [524], 'Oden': [526], 'JT.': [527], 'h–p': [529], 'adaptive': [530], 'using': [532], 'clouds.': [533], '237–262.': [543], '6Oden': [544], 'JT,': [545], 'Duarte': [546], 'Zienkiewicz': [548], 'OC.': [549], 'new': [551, 572, 1029], 'cloud-based': [552], 'hp': [553], 'finite': [554, 593, 676, 984], 'element': [555, 629, 820, 985, 1461], '1998;': [564, 583, 641], '153:': [565], '117–126.': [566], '7Atluri': [567], 'SN,': [568], 'Zhu': [569], 'T.': [570, 626, 694, 837, 1027, 1106, 1129, 1199, 1309], 'Meshless': [573], 'Local': [574, 668], 'Petrov-Galerkin': [575], '(MLPG)': [576], 'approach': [577, 1109], 'mechanics.': [580, 633, 1601], 'Computational': [581, 595, 848, 1099, 1513], '22:': [584], '117–127.': [585], '8De': [586], 'Bathe': [588], 'KJ.': [589], 'spheres.': [594], '2000;': [597, 735, 878, 897], '24:': [598], '329–345.': [599], '9Braun': [600], 'J,': [601, 835, 854, 1371], 'Sambridge': [602], 'M.': [603, 667, 792, 1375], 'numerical': [605, 1009, 1616], 'solving': [608], 'partial': [609], 'differential': [610], 'equations': [611, 1621], 'highly': [613], 'irregular': [614], 'evolving': [615], 'grids.': [616], 'Nature': [617], '376:': [619], '655–660.': [620], '10Sukumar': [621], 'N,': [622], 'Moran': [623, 1153, 1522], 'B,': [624, 1154, 1224, 1523], 'Belytschko': [625, 693, 836, 902, 1026, 1128, 1198, 1308], 'natural': [628], 'solid': [632, 1600], '43:': [642], '839–887.': [643], '11Sukumar': [644], 'N.': [645], 'Construction': [646], 'polygonal': [648], 'interpolants:': [649], 'maximum': [651], 'entropy': [652], 'approach.': [653, 1465], '2004;': [661, 920, 1172, 1331], '61:': [662], '2159–2181.': [663], '12Arroyo': [664], 'M,': [665, 790, 951, 975, 1082], 'Ortiz': [666], 'maximum-entropy': [669], 'approximation': [670], 'schemes:': [671], 'seamless': [673], 'bridge': [674], 'between': [675], 'elements': [677], '2006;': [688], '65:': [689], '2167–2202.': [690], '13Beissel': [691], 'Nodal': [695], '49–74.': [711], '14Belytschko': [712], 'Guo': [714], 'Y,': [715, 1025, 1365, 1425], 'Xiao': [718, 904], 'SP.': [719, 905], 'unified': [721], 'meshless': [725, 775, 1012, 1108], '48:': [736, 898], '1359–1400.': [737], '15Chen': [738], 'Yoon': [742, 925], 'You': [744], 'Y.': [745], 'stabilized': [747, 932], 'conforming': [748, 933, 1158], 'mesh-free': [753, 1037, 1137], '2001;': [762], '50:': [763], '435–466.': [764], '16Babuška': [765], 'I,': [766, 815, 1000], 'Banerjee': [767, 1001], 'U,': [768, 1002], 'Osborn': [769, 1003], 'JE,': [770, 1004], 'Li': [771, 1005, 1057, 1194, 1225], 'Q.': [772, 1006], 'Quadrature': [773], '2008;': [784, 996, 1148], '76:': [785], '1434–1470.': [786], '17Chen': [787], 'Rüter': [791], 'arbitrary': [794], '2013;': [811, 1359], '95:': [812], '387–418.': [813], '18Kaljević': [814], 'Saigal': [816], 'S.': [817, 856], 'improved': [819], 'free': [821], 'formulation.': [823, 1245], '1997;': [831], '40:': [832], '2953–2974.': [833], '19Dolbow': [834], 'weak': [843], 'form': [844], '1999;': [850, 1123, 1278, 1301], '23:': [851, 972], '219–230.': [852], '20Bonet': [853], 'Kulasegaram': [855], 'Correction': [857], 'smooth': [861], 'hydrodynamics': [863], 'applications': [866, 1112], 'metal': [868], 'forming': [869], 'simulations.': [870], '47:': [879], '1189–1214.': [880], '21Randles': [881], 'PW,': [882], 'Libersky': [883], 'LD.': [884], 'Normalized': [885], 'SPH': [886], 'stress': [888], 'points.': [889], '1445–1462.': [899], '22Rabczuk': [900], 'Stable': [906], 'Lagrangian': [911], 'kernels.': [912], '193:': [921, 1332], '1035–1063.': [922], '23Chen': [923], 'CT.': [928], 'Nonlinear': [929], '2002;': [947, 971], '53:': [948, 1474], '2587–2615.': [949], '24Griebel': [950], 'Schweitzer': [952, 1449], 'MA.': [953], 'particle-partition': [955], 'unity': [957, 1265, 1290], 'method–part': [958], 'II:': [959, 1292], 'cover': [961], 'construction': [962], 'reliable': [964], 'SIAM': [966], 'Scientific': [969], 'Computing': [970], '1655–1682.': [973], '25Puso': [974], 'Zywicz': [978], 'E,': [979], 'Elmer': [980], 'W.': [981], 'Meshfree': [982, 1439], '74:': [997, 1149], '416–446.': [998], '26Babuška': [999], 'Effect': [1007], '2009;': [1021, 1389, 1497], '198:': [1022], '2886–2897.': [1023], '27Liu': [1024], 'support': [1030], 'weakform': [1035], '2010;': [1046], '82:': [1047], '699–715.': [1048], '28Liu': [1049], 'GR,': [1050], 'GY,': [1052, 1058], 'Wang': [1053, 1223], 'Zhong': [1055], 'ZH,': [1056], 'Han': [1059], 'X.': [1060, 1427], 'technique': [1064], 'radial': [1067], 'point': [1068], 'interpolation': [1069], '(NI-RPIM).': [1071], 'Solids': [1075, 1542], 'Structures': [1077], '2007;': [1078], '44:': [1079, 1586], '3840–3890.': [1080], '29Hillman': [1081], 'Chi': [1085, 1394], 'SW.': [1086], 'Stabilized': [1087, 1157], 'modeling': [1095, 1382], 'impact': [1097], 'Particle': [1100], '2014;': [1102, 1253], '1:': [1103], '245–256.': [1104], '30Nagashima': [1105], 'Node-by-node': [1107], 'its': [1111], 'structural': [1114], 'analyses.': [1115], '46:': [1124], '341–385.': [1125], '31Fries': [1126], 'TP,': [1127], 'Convergence': [1130], 'stress-point': [1134], '1067–1087.': [1150], '32Yoo': [1151], 'JW,': [1152], 'JS.': [1156, 1481], 'natural-element': [1163], '60:': [1173], '861–890.': [1174], '33Strang': [1175], 'G,': [1176], 'Fix': [1177], 'G.': [1178, 1547], 'Analysis': [1180], 'Finite': [1183, 1460, 1612], 'Element': [1184], 'Method': [1185], '(2nd': [1186], 'edn.)': [1187], 'Wellesley-Cambridge': [1188], 'Press:': [1189], 'Massachusetts,': [1190], '2008.': [1191], '34Duan': [1192], 'Q,': [1193, 1220], 'X,': [1195, 1222, 1226, 1307], 'H,': [1197, 1369], 'Second-order': [1200], 'accurate': [1201], 'derivatives': [1202], 'schemes': [1205], '2012;': [1216], '92:': [1217], '399–424.': [1218], '35Duan': [1219], 'Gao': [1221], 'H.': [1228], 'four-point': [1230], 'quadratic': [1234], 'exactness': [1235], 'three-dimensional': [1237], '280:': [1254], '84–116.': [1255], '36Li': [1256], 'hierarchical': [1262, 1287], 'partition': [1263, 1288], 'part': [1266, 1291], 'I:': [1267], 'formulation': [1268, 1380], 'theory.': [1270], '45:': [1279, 1302], '251–288.': [1280], '37Li': [1281], 'applications.': [1293], '289–317.': [1303], '38Chen': [1304], 'gradient': [1312, 1343], 'model': [1313], 'strain': [1318, 1321], 'regularization': [1319, 1433], 'localization': [1322], '2827–2844.': [1333], '39Chi': [1334], 'SW,': [1335, 1395], 'Hu': [1338, 1420], 'HY,': [1339, 1477], 'Yang': [1340], 'JP.': [1341], 'collocation': [1346, 1491], 'boundary': [1349], 'value': [1350], '93:': [1360], '1381–1402.': [1361], '40Chen': [1362], 'Guan': [1366], 'PC,': [1367, 1393], 'Teng': [1368], 'Gaidos': [1370], 'Hofstetter': [1372], 'K,': [1373], 'Alsaleh': [1374], 'semi-Lagrangian': [1377], 'earth': [1383], 'moving': [1384], 'operations.': [1385], 'Materials': [1388], '41:': [1390], '670–683.': [1391], '41Guan': [1392], 'Slawson': [1398], 'TR,': [1399], 'Roth': [1400], 'MJ.': [1401], 'Semi-Lagrangian': [1402], 'fragment-impact': [1408], 'Impact': [1413, 1575], '2011;': [1415], '38:': [1416], '1033–1047.': [1417], '42Chen': [1418], 'W,': [1421], 'Puso': [1422], 'MA,': [1423], 'Strain': [1428], 'smoothing': [1429], 'Partial': [1442, 1507], 'Differential': [1443, 1508], 'Equations': [1444], 'III,': [1445], 'M': [1446], 'Griebel,': [1447], 'MA': [1448], '(eds).Springer:': [1450], 'Berlin;': [1451], '57–75,': [1452], '2007.': [1453], '43Liu': [1454], 'Ong': [1456], 'JSJ,': [1457], 'Uras': [1458], 'RA.': [1459], 'matrices-a': [1463], 'unification': [1464], '1985;': [1473], '13–46.': [1475], '44Hu': [1476], 'Lai': [1478], 'CK,': [1479], 'study': [1483], 'Interaction': [1493], 'Multiscale': [1495], '2:': [1498], '295–319.': [1499], '45Quarteroni': [1500], 'A,': [1501], 'Valli': [1502], 'A.': [1503], 'Approximation': [1505], 'Equations,': [1509], 'Springer': [1510], 'Series': [1511], 'Mathematics,': [1514], 'vol.': [1515], '23.': [1516], 'Springer:': [1517], 'Berlin,': [1518], '1994.': [1519], '46Norris': [1520], 'DM,': [1521], 'Scudder': [1524], 'JK,': [1525], 'Quinones': [1526], 'DF.': [1527], 'computer': [1529], 'simulation': [1530], 'tension': [1533], 'test.': [1534], 'Physics': [1540, 1584, 1603], '1978;': [1543], '26:': [1544], '1–19.': [1545], '47Taylor': [1546], 'use': [1549], 'flat-ended': [1551], 'projectiles': [1552], 'determining': [1554], 'dynamic': [1555], 'stress,': [1557], 'Part': [1558], 'I.': [1559], 'Proceedings': [1560], 'Royal': [1563], 'Society': [1564], 'London': [1566], '1948;': [1568], '194:': [1569], '289–299.': [1570], '48Wilkins': [1571], 'ML,': [1572], 'Guinan': [1573], 'MW.': [1574], 'cylinders': [1577], 'rigid': [1579], 'boundary.': [1580], '1973;': [1585], '1200–1206.': [1587], '49Sulsky': [1588], 'D,': [1589], 'Zhou': [1590], 'SJ,': [1591], 'Schreyer': [1592], 'HL.': [1593], 'Application': [1594], 'particle-in-cell': [1597], 'Communications': [1604], '87:': [1606], '236–252.': [1607], '50Hughes': [1608], 'TJ,': [1609], 'Winget': [1610], 'J.': [1611], 'rotation': [1613], 'effects': [1614], 'rate': [1619], 'constitutive': [1620], 'arising': [1622], 'large-deformation': [1624], 'analysis.': [1625], '1980;': [1633], '15:': [1634], '1862–1867.': [1635], 'Citing': [1636], 'Literature': [1637], 'Volume107,': [1638], 'Issue717': [1639], 'August': [1640], '2016Pages': [1641], 'ReferencesRelatedInformation': [1643]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2262053990', 'counts_by_year': [{'year': 2024, 'cited_by_count': 20}, {'year': 2023, 'cited_by_count': 26}, {'year': 2022, 'cited_by_count': 20}, {'year': 2021, 'cited_by_count': 23}, {'year': 2020, 'cited_by_count': 14}, {'year': 2019, 'cited_by_count': 20}, {'year': 2018, 'cited_by_count': 7}, {'year': 2017, 'cited_by_count': 6}, {'year': 2016, 'cited_by_count': 1}], 'updated_date': '2024-09-12T15:42:52.005396', 'created_date': '2016-06-24'}