id sid eid entity type cana-4511 1 1 1074 CARDINAL cana-4511 1 2 32 CARDINAL cana-4511 2 1 9s CARDINAL cana-4511 2 2 2025 CARDINAL cana-4511 2 3 2258 CARDINAL cana-4511 3 1 linear ORG cana-4511 3 2 shinde1 PERSON cana-4511 3 3 dr. PERSON cana-4511 3 4 khankal2 PERSON cana-4511 4 1 s. k. agarwal3 PERSON cana-4511 5 1 ph.d NORP cana-4511 5 2 sinhgad college of engineering ORG cana-4511 5 3 pune GPE cana-4511 5 4 2 CARDINAL cana-4511 6 1 sinhgad college ORG cana-4511 6 2 pune GPE cana-4511 6 3 maharashtra GPE cana-4511 6 4 3 CARDINAL cana-4511 7 1 pune GPE cana-4511 7 2 maharashtra GPE cana-4511 7 3 india GPE cana-4511 7 4 12-01-2025 CARDINAL cana-4511 7 5 15-02-2025 CARDINAL cana-4511 7 6 01-03-2025 CARDINAL cana-4511 23 1 winkler ORG cana-4511 23 2 linear ORG cana-4511 27 1 zero CARDINAL cana-4511 27 2 non-linear LOC cana-4511 27 3 two CARDINAL cana-4511 27 4 linear ORG cana-4511 28 1 boef GPE cana-4511 29 1 1074 CARDINAL cana-4511 29 2 32 CARDINAL cana-4511 30 1 9s CARDINAL cana-4511 30 2 2025 DATE cana-4511 30 3 2259 CARDINAL cana-4511 32 1 indian NORP cana-4511 32 2 60 kg QUANTITY cana-4511 32 3 52 kg QUANTITY cana-4511 33 1 1 CARDINAL cana-4511 35 1 winkler ORG cana-4511 35 2 linear ORG cana-4511 38 1 zimmermann PERSON cana-4511 38 2 1888 DATE cana-4511 38 3 the winkler hypothesis ORG cana-4511 38 4 1 CARDINAL cana-4511 39 1 1970 DATE cana-4511 39 2 meacham et ORG cana-4511 40 1 al PERSON cana-4511 41 1 1970 DATE cana-4511 41 2 spring DATE cana-4511 42 1 lundgren PERSON cana-4511 42 2 martin PERSON cana-4511 42 3 1970 DATE cana-4511 42 4 thompson PERSON cana-4511 42 5 1976 DATE cana-4511 44 1 al PERSON cana-4511 44 2 1978 DATE cana-4511 45 1 linear ORG cana-4511 45 2 one CARDINAL cana-4511 45 3 two degrees QUANTITY cana-4511 47 1 kerr ORG cana-4511 47 2 1976 DATE cana-4511 47 3 2 CARDINAL cana-4511 47 4 19 CARDINAL cana-4511 48 1 hetenyi ORG cana-4511 49 1 21 CARDINAL cana-4511 50 1 sandeep shinde et PERSON cana-4511 51 1 al PERSON cana-4511 52 1 2020 DATE cana-4511 53 1 1 CARDINAL cana-4511 54 1 dahlberg PERSON cana-4511 55 1 2 CARDINAL cana-4511 55 2 1074 CARDINAL cana-4511 55 3 32 CARDINAL cana-4511 56 1 9s CARDINAL cana-4511 56 2 2260 CARDINAL cana-4511 56 3 3-d QUANTITY cana-4511 56 4 2 CARDINAL cana-4511 57 1 boef PERSON cana-4511 57 2 euler-bernoulli beam ORG cana-4511 60 1 winkler GPE cana-4511 60 2 1867 DATE cana-4511 60 3 euler-bernoulli ORG cana-4511 61 1 2 CARDINAL cana-4511 61 2 boef ORG cana-4511 61 3 3 CARDINAL cana-4511 61 4 2.1 CARDINAL cana-4511 62 1 2 CARDINAL cana-4511 66 1 3 CARDINAL cana-4511 69 1 2 CARDINAL cana-4511 69 2 1 CARDINAL cana-4511 70 1 4 CARDINAL cana-4511 70 2 2 CARDINAL cana-4511 70 3 1/4 CARDINAL cana-4511 70 4 3 CARDINAL cana-4511 70 5 second ORDINAL cana-4511 71 1 1074 CARDINAL cana-4511 71 2 32 CARDINAL cana-4511 72 1 9s CARDINAL cana-4511 72 2 2025 CARDINAL cana-4511 72 3 2261 CARDINAL cana-4511 74 1 three CARDINAL cana-4511 74 2 40-50% PERCENT cana-4511 78 1 approximately 800-1000 QUANTITY cana-4511 79 1 2 CARDINAL cana-4511 79 2 3 CARDINAL cana-4511 84 1 2.2 CARDINAL cana-4511 84 2 two CARDINAL cana-4511 84 3 4 CARDINAL cana-4511 88 1 one CARDINAL cana-4511 88 2 4 CARDINAL cana-4511 89 1 fpp PERSON cana-4511 90 1 4 CARDINAL cana-4511 91 1 two CARDINAL cana-4511 93 1 1074 CARDINAL cana-4511 93 2 32 CARDINAL cana-4511 94 1 9s CARDINAL cana-4511 94 2 2025 CARDINAL cana-4511 94 3 2262 DATE cana-4511 98 1 three CARDINAL cana-4511 98 2 between 30.0 CARDINAL cana-4511 98 3 2000.0 CARDINAL cana-4511 98 4 4 CARDINAL cana-4511 98 5 spring DATE cana-4511 98 6 spring DATE cana-4511 98 7 mass GPE cana-4511 98 8 spring DATE cana-4511 99 1 one CARDINAL cana-4511 99 2 one CARDINAL cana-4511 100 1 3 CARDINAL cana-4511 100 2 2 CARDINAL cana-4511 100 3 3 CARDINAL cana-4511 101 1 2 CARDINAL cana-4511 101 2 π’…π’™πŸ CARDINAL cana-4511 104 1 5 CARDINAL cana-4511 104 2 w GPE cana-4511 105 1 dz/dx ORG cana-4511 107 1 5 CARDINAL cana-4511 107 2 w ORG cana-4511 107 3 one CARDINAL cana-4511 110 1 3 CARDINAL cana-4511 111 1 5 CARDINAL cana-4511 113 1 6 CARDINAL cana-4511 113 2 1074 CARDINAL cana-4511 113 3 32 CARDINAL cana-4511 114 1 9s CARDINAL cana-4511 114 2 2025 CARDINAL cana-4511 114 3 2263 DATE cana-4511 114 4 1 CARDINAL cana-4511 116 1 5 CARDINAL cana-4511 117 1 5 CARDINAL cana-4511 117 2 6 CARDINAL cana-4511 117 3 first ORDINAL cana-4511 118 1 eqn PERSON cana-4511 118 2 four CARDINAL cana-4511 118 3 first ORDINAL cana-4511 118 4 𝟎 𝟏 𝟎 𝟎 𝟎 𝟏 QUANTITY cana-4511 118 5 𝟎 PRODUCT cana-4511 118 6 𝟎 𝟎 𝟎 𝟎 𝟎 𝟏 𝟎 TIME cana-4511 118 7 π’€πŸ π’€πŸ DATE cana-4511 119 1 π’€πŸ CARDINAL cana-4511 119 2 πŸ•π’‚ CARDINAL cana-4511 119 3 πŸ•π’ƒ CARDINAL cana-4511 119 4 π‘©π’†π’π’…π’Šπ’π’ˆ π‘΄π’π’Žπ’†π’π’• PERSON cana-4511 120 1 𝑺𝒉𝒆𝒂𝒓 PERSON cana-4511 120 2 πŸ•π’… CARDINAL cana-4511 122 1 first ORDINAL cana-4511 122 2 1074 CARDINAL cana-4511 122 3 32 CARDINAL cana-4511 124 1 9s CARDINAL cana-4511 124 2 2025 CARDINAL cana-4511 124 3 2264 DATE cana-4511 124 4 first ORDINAL cana-4511 125 1 a foundation spring DATE cana-4511 125 2 the spring DATE cana-4511 125 3 the spring DATE cana-4511 126 1 the spring DATE cana-4511 126 2 zero CARDINAL cana-4511 127 1 the spring DATE cana-4511 128 1 second ORDINAL cana-4511 129 1 zero CARDINAL cana-4511 129 2 a spring DATE cana-4511 130 1 two CARDINAL cana-4511 131 1 first ORDINAL cana-4511 131 2 πŸ– CARDINAL cana-4511 132 1 πŸ— CARDINAL cana-4511 132 2 4 CARDINAL cana-4511 132 3 euler-bernoulli PERSON cana-4511 132 4 boef GPE cana-4511 132 5 boef GPE cana-4511 132 6 thompson PERSON cana-4511 133 1 5 CARDINAL cana-4511 133 2 6 DATE cana-4511 133 3 7 DATE cana-4511 133 4 8 CARDINAL cana-4511 134 1 ansys ORG cana-4511 135 1 the uic60 cross section ORG cana-4511 135 2 indian NORP cana-4511 135 3 7 CARDINAL cana-4511 135 4 7 CARDINAL cana-4511 135 5 mm PERSON cana-4511 135 6 4.1 CARDINAL cana-4511 136 1 non – linear ORG cana-4511 138 1 mooney PERSON cana-4511 138 2 rivlin PERSON cana-4511 139 1 1074 CARDINAL cana-4511 139 2 32 CARDINAL cana-4511 140 1 9s CARDINAL cana-4511 140 2 2025 CARDINAL cana-4511 140 3 2265 DATE cana-4511 144 1 8 CARDINAL cana-4511 144 2 ansys PERSON cana-4511 148 1 3rd ORDINAL cana-4511 150 1 10 CARDINAL cana-4511 150 2 n. n= 3, ORG cana-4511 150 3 c01 ORG cana-4511 150 4 c02 GPE cana-4511 150 5 c30 ORG cana-4511 150 6 c21 GPE cana-4511 150 7 c12 ORG cana-4511 151 1 ansys ORG cana-4511 152 1 ansys ORG cana-4511 152 2 one CARDINAL cana-4511 154 1 first ORDINAL cana-4511 154 2 second ORDINAL cana-4511 154 3 j= GPE cana-4511 154 4 1074 CARDINAL cana-4511 154 5 32 CARDINAL cana-4511 156 1 9s CARDINAL cana-4511 156 2 2025 CARDINAL cana-4511 156 3 2266 CARDINAL cana-4511 157 1 9 CARDINAL cana-4511 162 1 0.256580 CARDINAL cana-4511 163 1 11 CARDINAL cana-4511 163 2 kp ORG cana-4511 164 1 0.4337 CARDINAL cana-4511 164 2 12 CARDINAL cana-4511 164 3 4.2 CARDINAL cana-4511 165 1 euler-bernoulli PERSON cana-4511 165 2 boef GPE cana-4511 165 3 60 kg QUANTITY cana-4511 165 4 36 CARDINAL cana-4511 166 1 the spring DATE cana-4511 167 1 two CARDINAL cana-4511 167 2 0.6 m. PERSON cana-4511 167 3 boef GPE cana-4511 167 4 ansys ORG cana-4511 168 1 leposava PERSON cana-4511 168 2 14 CARDINAL cana-4511 169 1 boef GPE cana-4511 169 2 sandeep shinde et PERSON cana-4511 170 1 al PERSON cana-4511 171 1 25 CARDINAL cana-4511 172 1 2010 DATE cana-4511 172 2 alazzawi et PERSON cana-4511 173 1 al PERSON cana-4511 174 1 26 CARDINAL cana-4511 175 1 10 CARDINAL cana-4511 175 2 1 CARDINAL cana-4511 175 3 1074 CARDINAL cana-4511 175 4 32 CARDINAL cana-4511 177 1 9s CARDINAL cana-4511 177 2 2025 CARDINAL cana-4511 177 3 2267 DATE cana-4511 177 4 0 CARDINAL cana-4511 177 5 250 kn QUANTITY cana-4511 178 1 the linear spring DATE cana-4511 180 1 4.3 CARDINAL cana-4511 180 2 boef GPE cana-4511 181 1 non-linear LOC cana-4511 182 1 11 CARDINAL cana-4511 182 2 linear ORG cana-4511 182 3 non-linear ORG cana-4511 182 4 ansys ORG cana-4511 182 5 3.65% PERCENT cana-4511 183 1 ansys ORG cana-4511 183 2 3.88% PERCENT cana-4511 184 1 linear ORG cana-4511 184 2 2 CARDINAL cana-4511 184 3 2 CARDINAL cana-4511 185 1 3.047 CARDINAL cana-4511 185 2 107 CARDINAL cana-4511 185 3 3.047 CARDINAL cana-4511 185 4 60 CARDINAL cana-4511 185 5 πŸπ‘² PERSON cana-4511 185 6 boef GPE cana-4511 186 1 πŸ’ CARDINAL cana-4511 186 2 𝟏. CARDINAL cana-4511 186 3 0.1043 mm QUANTITY cana-4511 186 4 0.2087 mm PERSON cana-4511 186 5 0.3131 mm y4= 0.4175 PERSON cana-4511 187 1 0.5218 mm y6= PERSON cana-4511 187 2 0.6262 mm QUANTITY cana-4511 188 1 0.835 mm QUANTITY cana-4511 189 1 0.9393 mm QUANTITY cana-4511 189 2 1.043 mm QUANTITY cana-4511 189 3 ansys PERSON cana-4511 189 4 1074 CARDINAL cana-4511 189 5 32 CARDINAL cana-4511 190 1 9s CARDINAL cana-4511 190 2 2025 CARDINAL cana-4511 190 3 2268 CARDINAL cana-4511 190 4 12 CARDINAL cana-4511 190 5 ansys PERSON cana-4511 190 6 11 CARDINAL cana-4511 191 1 13 CARDINAL cana-4511 191 2 linear ORG cana-4511 191 3 14 CARDINAL cana-4511 191 4 1074 CARDINAL cana-4511 191 5 32 CARDINAL cana-4511 193 1 9s CARDINAL cana-4511 193 2 2025 CARDINAL cana-4511 193 3 2269 CARDINAL cana-4511 193 4 5 CARDINAL cana-4511 194 1 14 CARDINAL cana-4511 194 2 1 CARDINAL cana-4511 195 1 2 CARDINAL cana-4511 195 2 3.4 mm QUANTITY cana-4511 195 3 approximately three CARDINAL cana-4511 195 4 linear ORG cana-4511 195 5 1.08 mm QUANTITY cana-4511 196 1 3 CARDINAL cana-4511 196 2 approximately three CARDINAL cana-4511 196 3 linear ORG cana-4511 196 4 0.08 mm QUANTITY cana-4511 197 1 4 CARDINAL cana-4511 197 2 zero CARDINAL cana-4511 197 3 4.28 m QUANTITY cana-4511 197 4 approximately two CARDINAL cana-4511 197 5 linear ORG cana-4511 198 1 5 CARDINAL cana-4511 198 2 zero CARDINAL cana-4511 198 3 approximately two CARDINAL cana-4511 198 4 linear ORG cana-4511 198 5 1.0 CARDINAL cana-4511 199 1 6 CARDINAL cana-4511 199 2 12.5 CARDINAL cana-4511 199 3 approximately three CARDINAL cana-4511 199 4 linear ORG cana-4511 199 5 4.0 mm QUANTITY cana-4511 200 1 6 CARDINAL cana-4511 200 2 1 CARDINAL cana-4511 200 3 valji shinde PERSON cana-4511 200 4 dr. PERSON cana-4511 200 5 s. s. PERSON cana-4511 201 1 s. k. agarwal PERSON cana-4511 201 2 13 CARDINAL cana-4511 201 3 3s CARDINAL cana-4511 201 4 2020 DATE cana-4511 203 1 2 CARDINAL cana-4511 203 2 d.r. GPE cana-4511 203 3 h.c. GPE cana-4511 203 4 meacham PERSON cana-4511 203 5 r.h. prause PERSON cana-4511 203 6 a.d. kerr PERSON cana-4511 203 7 ed PERSON cana-4511 203 8 mechanics & technology ORG cana-4511 203 9 pergamon press ORG cana-4511 203 10 oxford GPE cana-4511 203 11 1978 DATE cana-4511 204 1 3 CARDINAL cana-4511 204 2 dahlberg PERSON cana-4511 204 3 sweden GPE cana-4511 204 4 2003 DATE cana-4511 205 1 4 CARDINAL cana-4511 205 2 esveld c. PERSON cana-4511 205 3 2nd ORDINAL cana-4511 205 4 netherlands GPE cana-4511 205 5 2001 DATE cana-4511 206 1 5 CARDINAL cana-4511 206 2 203 CARDINAL cana-4511 206 3 1989 DATE cana-4511 206 4 97 CARDINAL cana-4511 207 1 6 CARDINAL cana-4511 207 2 alexander remennikov PERSON cana-4511 207 3 university of wollongong ORG cana-4511 207 4 australia GPE cana-4511 207 5 2009 DATE cana-4511 207 6 7 CARDINAL cana-4511 207 7 wu y. PERSON cana-4511 207 8 68 CARDINAL cana-4511 207 9 1998 DATE cana-4511 207 10 457-470 QUANTITY cana-4511 207 11 8 CARDINAL cana-4511 207 12 thompson d.j. PERSON cana-4511 207 13 van vliet w.j. PERSON cana-4511 207 14 j.w. GPE cana-4511 207 15 213(1 CARDINAL cana-4511 207 16 1998 DATE cana-4511 207 17 169-188 CARDINAL cana-4511 208 1 9 CARDINAL cana-4511 208 2 thompson d.j. PERSON cana-4511 208 3 jones c.j.c PERSON cana-4511 208 4 wu t.x. PERSON cana-4511 208 5 france GPE cana-4511 208 6 213 CARDINAL cana-4511 208 7 1999 DATE cana-4511 208 8 233-241 CARDINAL cana-4511 209 1 10 CARDINAL cana-4511 209 2 hong xiao PERSON cana-4511 209 3 jia-bin wang PERSON cana-4511 209 4 yan-rong zhang PERSON cana-4511 209 5 2017 CARDINAL cana-4511 209 6 1074 CARDINAL cana-4511 209 7 32 CARDINAL cana-4511 210 1 9s CARDINAL cana-4511 210 2 2025 CARDINAL cana-4511 210 3 2270 DATE cana-4511 211 1 11 CARDINAL cana-4511 211 2 samuel g. coroma PERSON cana-4511 211 3 mohommad fm hussein PERSON cana-4511 211 4 john s. owen PERSON cana-4511 212 1 12 CARDINAL cana-4511 212 2 shane crawford PERSON cana-4511 212 3 martin murray PERSON cana-4511 212 4 john powell PERSON cana-4511 212 5 7th ORDINAL cana-4511 212 6 brisbane GPE cana-4511 212 7 australia GPE cana-4511 212 8 2001 DATE cana-4511 213 1 13 CARDINAL cana-4511 213 2 k. ganesh babu PERSON cana-4511 213 3 c. sujatha PERSON cana-4511 213 4 10.1177/107754639341600, 2009 DATE cana-4511 214 1 14 CARDINAL cana-4511 214 2 university of belgrade ORG cana-4511 214 3 serbia GPE cana-4511 214 4 2012 DATE cana-4511 214 5 no.5 ORG cana-4511 214 6 405 CARDINAL cana-4511 214 7 2012 DATE cana-4511 215 1 15 CARDINAL cana-4511 215 2 s. s. PERSON cana-4511 216 1 s. k. agarwal PERSON cana-4511 216 2 sumit patil PERSON cana-4511 216 3 anup yeole PERSON cana-4511 216 4 shubham jain GPE cana-4511 216 5 2019 DATE cana-4511 216 6 pune GPE cana-4511 216 7 3021 CARDINAL cana-4511 217 1 16 CARDINAL cana-4511 217 2 j. clastornik PERSON cana-4511 217 3 m. eisenberger PERSON cana-4511 217 4 d.z. yankelevsky PERSON cana-4511 217 5 m.a. adin PERSON cana-4511 217 6 winkler elastic foundation ORG cana-4511 217 7 53 CARDINAL cana-4511 217 8 4 CARDINAL cana-4511 217 9 1986 DATE cana-4511 217 10 925–928 CARDINAL cana-4511 218 1 17 CARDINAL cana-4511 218 2 2nd ORDINAL cana-4511 218 3 congress ORG cana-4511 218 4 zurich GPE cana-4511 218 5 14th – 16th september 1926 DATE cana-4511 218 6 18 CARDINAL cana-4511 218 7 avramidis PERSON cana-4511 218 8 k. morfidis PERSON cana-4511 218 9 three CARDINAL cana-4511 218 10 43 CARDINAL cana-4511 218 11 2006 DATE cana-4511 218 12 357–375 CARDINAL cana-4511 218 13 19 CARDINAL cana-4511 218 14 kerr ORG cana-4511 218 15 31 CARDINAL cana-4511 218 16 3 CARDINAL cana-4511 218 17 1964 DATE cana-4511 218 18 491–498 CARDINAL cana-4511 219 1 20 CARDINAL cana-4511 219 2 f. zhaohua PERSON cana-4511 219 3 r.d. cook PERSON cana-4511 219 4 two CARDINAL cana-4511 219 5 109 CARDINAL cana-4511 219 6 6 CARDINAL cana-4511 219 7 1983 DATE cana-4511 219 8 1390–1402 DATE cana-4511 220 1 21 CARDINAL cana-4511 220 2 m. hetenyi PERSON cana-4511 220 3 21 CARDINAL cana-4511 220 4 1950 DATE cana-4511 220 5 55–58 CARDINAL cana-4511 221 1 22 CARDINAL cana-4511 221 2 m. beams PERSON cana-4511 222 1 ann arbor: PERSON cana-4511 222 2 1202 CARDINAL cana-4511 222 3 1946 DATE cana-4511 222 4 23 CARDINAL cana-4511 223 1 two CARDINAL cana-4511 224 1 gosuderevstvennae PERSON cana-4511 224 2 1289 CARDINAL cana-4511 225 1 moscow GPE cana-4511 225 2 ussr GPE cana-4511 225 3 1954 DATE cana-4511 226 1 24 CARDINAL cana-4511 226 2 valji shinde PERSON cana-4511 226 3 dr. PERSON cana-4511 226 4 s. s. PERSON cana-4511 226 5 s. k. agarwal PERSON cana-4511 226 6 mukt shabd journal ORG cana-4511 226 7 vi PERSON cana-4511 226 8 25 CARDINAL cana-4511 226 9 valji shinde PERSON cana-4511 226 10 dr. PERSON cana-4511 226 11 s. s. PERSON cana-4511 227 1 s. k. agarwal PERSON cana-4511 227 2 2020 DATE cana-4511 227 3 26 CARDINAL cana-4511 227 4 a. a. alazzawi PERSON cana-4511 227 5 a. h. mahdy PERSON cana-4511 227 6 farhan PERSON cana-4511 227 7 serbian NORP cana-4511 228 1 2, 2010 DATE cana-4511 230 1 13-42 CARDINAL