Константинов Н.А., Лалин В.В., Лалина И.И. - Расчёт статически определимых стержневых систем с использованием SCAD, страница 8
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ȼɫɟɝɨ ɩɪɢɪɟɲɟɧɢɢ ɡɚɞɚɱɢ ɨɛ ɇȾɋ ɮɟɪɦɵ ɛɭɞɟɦ ɢɦɟɬɶ nɧnɫ nɨɩ ɧɟɢɡɜɟɫɬɧɵɯ ɭɫɢɥɢɣ.ȼɫɟ ɷɬɢ ɭɫɢɥɢɹ ɞɟɣɫɬɜɭɸɬ ɧɚ ɭɡɥɵ ɮɟɪɦɵ ɱɢɫɥɨɦ nɭ .Ⱦɥɹ ɤɚɠɞɨɝɨ ɭɡɥɚ i ɮɟɪɦɵ ɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɞɜɚ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ. ȼɫɢɫɬɟɦɟ ɈɋɄ, ɤɨɬɨɪɚɹ ɢɡɨɛɪɚɠɟɧɚ ɧɚ ɪɢɫ. 1.2, ɠ, ɨɧɢ ɦɨɝɭɬ ɛɵɬɶ ɩɪɟɞɫɬɚɜɥɟɧɵɜ ɜɢɞɟ (2.22).ȼ ɰɟɧɬɪɟ ɭɡɥɚ ɩɟɪɟɫɟɤɚɸɬɫɹ ɥɢɧɢɢ ɞɟɣɫɬɜɢɹ ɜɫɟɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚɭɡɟɥ. ɉɨɷɬɨɦɭ ɬɪɟɬɶɟ ɭɪɚɜɧɟɧɢɟ ɪɚɜɧɨɜɟɫɢɹ ɭɡɥɚ, ɢɦɟɸɳɟɟ ɜɢɞ ɪɚɜɟɧɫɬɜɚ ɧɭɥɸɦɨɦɟɧɬɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɰɟɧɬɪɚ ɭɡɥɚ, ɭɞɨɜɥɟɬɜɨɪɹɟɬɫɹ ɬɨɠɞɟɫɬɜɟɧɧɨ ɢ ɧɟ ɦɨɠɟɬɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɨ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ ɜ ɮɟɪɦɚɯ.nɭnɭ¦ X i 0; ¦ Z i 0 .i 1(2.22)i 1ȼɫɟɝɨ ɞɥɹ nɭ ɭɡɥɨɜ ɮɟɪɦɵ ɛɭɞɟɦ ɢɦɟɬɶ nɭɪ2nɭ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ.Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɤɪɨɦɟ ɮɨɪɦɭɥɵ (2.21) ɫɬɟɩɟɧɶ ɫɬɚɬɢɱɟɫɤɨɣ ɧɟɨɩɪɟɞɟɥɢɦɨɫɬɢɮɟɪɦ ɦɨɠɧɨ ɧɚɣɬɢ ɬɚɤɠɟ ɩɨ ɮɨɪɦɭɥɟɩ nɧ nɭɪ (nɫ nɨɩ ) 2nɭ .(2.23)ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɷɬɨɣ ɮɨɪɦɭɥɵ ɩɨɥɭɱɚɸɬɫɹ ɬɟ ɠɟ ɜɚɪɢɚɧɬɵɪɟɡɭɥɶɬɚɬɨɜ ɪɚɫɱɟɬɚ, ɤɨɬɨɪɵɟ ɨɩɢɫɚɧɵ ɞɥɹ ɮɨɪɦɭɥɵ (2.21).ɇɟɨɛɯɨɞɢɦɨɦɭ ɭɫɥɨɜɢɸ ɫɬɚɬɢɱɟɫɤɨɣ ɨɩɪɟɞɟɥɢɦɨɫɬɢ ɮɟɪɦɵ ɛɭɞɟɬɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɭɫɥɨɜɢɟ n 0 , ɤɨɬɨɪɨɦɭ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɪɚɜɟɧɫɬɜɨ ɱɢɫɥɚnɧ nɫ nɨɩ ɧɟɢɡɜɟɫɬɧɵɯ ɭɫɢɥɢɣ ɜ ɫɬɟɪɠɧɹɯ ɮɟɪɦɵ ɱɢɫɥɭ nɭɪ 2n ɭɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ ɭɡɥɨɜ ɜɢɞɚ (2.22).Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɧɟɨɛɯɨɞɢɦɨɝɨ ɭɫɥɨɜɢɹ n 0 ɮɟɪɦɚɛɵɥɚ ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɨɣ ɧɟɨɛɯɨɞɢɦɨ ɫɨɛɥɸɞɟɧɢɟɞɨɩɨɥɧɢɬɟɥɶɧɨɝɨ ɭɫɥɨɜɢɹ ɨ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɧɟɢɡɦɟɧɹɟɦɨɫɬɢ ɮɟɪɦɵ.
Ⱦɥɹ40ɩɪɨɫɬɟɣɲɢɯ ɩɨ ɨɛɪɚɡɨɜɚɧɢɸ ɮɟɪɦ ɷɬɨ Ƚɇ ɞɨɤɚɡɵɜɚɟɬɫɹ ɫɬɪɭɤɬɭɪɧɵɦ ɚɧɚɥɢɡɨɦɮɟɪɦɵ ɫ ɩɨɦɨɳɶɸ ɩɪɨɰɟɞɭɪɵ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɧɚɪɚɳɢɜɚɧɢɹ ɞɢɫɤɚ,ɩɪɟɞɫɬɚɜɥɹɸɳɟɝɨ ɮɟɪɦɭ, ɨɛɪɚɡɨɜɚɧɢɟɦ ɧɨɜɵɯ «ɬɪɟɭɝɨɥɶɧɵɯ» ɞɢɫɤɨɜ (ɫɦ. ɪɢɫ.2.1, ɛ, 5).ɉɪɢɦɟɪ 11. Ɏɟɪɦɚ, ɢɡɨɛɪɚɠɟɧɧɚɹ ɧɚ ɪɢɫ. 1.2, ɟ, 21.nɧȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɮɨɪɦɭɥɨɣ (2.23) ɢɦɟɟɦ:(nɫ nɨɩ ) (4 2 4 5) 3 20ɩ nɧ n ɭɪn ɭɪ2n ɭ2 10 20ɢ.(nɫ nɨɩ ) 2n ɭ = 0.ȼɵɩɨɥɧɹɟɬɫɹɧɟɨɛɯɨɞɢɦɨɟɭɫɥɨɜɢɟɫɬɚɬɢɱɟɫɤɨɣɨɩɪɟɞɟɥɢɦɨɫɬɢ ɮɟɪɦɵ.2.
ɋɬɪɭɤɬɭɪɧɵɣ ɚɧɚɥɢɡ ɮɟɪɦɵ, ɜɵɩɨɥɧɟɧɧɵɣ ɩɨɩɪɨɰɟɞɭɪɟ ɧɚɪɚɳɢɜɚɧɢɹ ɞɢɫɤɚ (ɫɦ. ɪɢɫ.2.1, ɛ, 5) ɩɨɤɚɡɵɜɚɟɬ, ɱɬɨɮɟɪɦɚ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨɛɨɣ ɟɞɢɧɵɣ ɞɢɫɤ. Ɉɧ ɧɟɩɨɞɜɢɠɧɨɩɪɢɤɪɟɩɥɟɧ ɤ ɨɫɧɨɜɚɧɢɸ ɬɪɟɦɹ ɫɜɹɡɹɦɢ, ɧɟ ɩɟɪɟɫɟɤɚɸɳɢɦɢɫɹ ɜɨɞɧɨɣ ɬɨɱɤɟ ɢ ɧɟ ɩɚɪɚɥɥɟɥɶɧɵɦɢ ɞɪɭɝ ɞɪɭɝɭ. Ɉɛɳɢɣ ɜɵɜɨɞ:ɮɟɪɦɚ ɫɬɚɬɢɱɟɫɤɢ ɨɩɪɟɞɟɥɢɦɚ.Ɋɚɫɫɦɨɬɪɟɧɧɵɟ ɩɪɨɫɬɵɟ ɩɪɢɟɦɵ ɫɬɪɭɤɬɭɪɧɨɝɨ ɚɧɚɥɢɡɚɊɢɫ.
2.11ɢɧɨɝɞɚ ɧɟ ɩɨɡɜɨɥɹɸɬ ɩɪɨɜɟɫɬɢ ɚɧɚɥɢɡ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣɧɟɢɡɦɟɧɹɟɦɨɫɬɢ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɟɫɥɢ ɨɧɚ ɨɛɪɚɡɨɜɚɧɚ ɛɨɥɟɟɫɥɨɠɧɵɦ ɫɩɨɫɨɛɨɦ.ɉɪɢɦɟɪɨɦ ɬɚɤɨɣ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ ɧɚ ɩɟɪɜɵɣ ɜɡɝɥɹɞ ɩɪɨɫɬɚɹ ɮɟɪɦɚ, ɢɡɨɛɪɚɠɟɧɧɚɹ ɧɚɪɢɫ. 2.11.Ɉɞɧɚɤɨ, ɧɚɱɚɬɶ ɫɬɪɭɤɬɭɪɧɵɣ ɚɧɚɥɢɡ ɷɬɨɣ ɮɟɪɦɵ ɩɭɬɟɦ ɨɛɪɚɡɨɜɚɧɢɹ ɞɢɫɤɚ ɜ ɜɢɞɟɬɪɟɭɝɨɥɶɧɢɤɚ ɧɟ ɭɞɚɟɬɫɹ.
Ɂɞɟɫɶ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɛɟɝɧɭɬɶ ɤ ɫɩɟɰɢɚɥɶɧɵɦ ɦɟɬɨɞɚɦɢɫɫɥɟɞɨɜɚɧɢɹ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɧɟɢɡɦɟɧɹɟɦɨɫɬɢ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ, ɨɞɢɧ ɢɡ ɤɨɬɨɪɵɯ ɛɭɞɟɬɪɚɫɫɦɨɬɪɟɧ ɜ ɩɨɞɪɚɡɞɟɥɟ 4.8 ɱɚɫɬɢ 2 ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ, ɩɨɫɥɟ ɢɡɭɱɟɧɢɹ ɫɩɨɫɨɛɨɜɨɩɪɟɞɟɥɟɧɢɹ ɭɫɢɥɢɣ ɜ ɫɬɟɪɠɧɹɯ ɮɟɪɦ.413. ɉɊȿȾȼȺɊɂɌȿɅɖɇɕȿ ɋȼȿȾȿɇɂə Ɉ ɊȺɋɑȿɌȿ ɋɌȿɊɀɇȿȼɕɏɋɂɋɌȿɆ ɆȿɌɈȾɈɆ ɄɈɇȿɑɇɕɏ ɗɅȿɆȿɇɌɈȼɋ ɂɋɉɈɅɖɁɈȼȺɇɂȿɆ ɉɊɈȽɊȺɆɆɕ SCAD3.1. ɉɪɟɞɫɬɚɜɥɟɧɢɟ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵɤɚɤ ɫɢɫɬɟɦɵ ɤɨɧɟɱɧɵɯ ɫɬɟɪɠɧɟɜɵɯ ɷɥɟɦɟɧɬɨɜɉɪɢ ɪɟɲɟɧɢɢ ɨɫɧɨɜɧɨɣ ɡɚɞɚɱɢ ɫɬɪɨɢɬɟɥɶɧɨɣ ɦɟɯɚɧɢɤɢ (ɨɩɪɟɞɟɥɟɧɢɟɩɟɪɟɦɟɳɟɧɢɣ, ɭɫɢɥɢɣ ɢ ɞɟɮɨɪɦɚɰɢɣ ɨɬ ɡɚɞɚɧɧɵɯ ɜɧɟɲɧɢɯ ɜɨɡɞɟɣɫɬɜɢɣ) ɞɥɹɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɦɟɬɨɞɨɦ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ (ɆɄɗ) ɢɯ ɩɪɟɞɫɬɚɜɥɹɸɬ ɤɚɤɫɢɫɬɟɦɵ ɬɢɩɨɜɵɯ ɫɬɟɪɠɧɟɜɵɯ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ (Ʉɗ), ɫɨɟɞɢɧɟɧɧɵɯ ɦɟɠɞɭɫɨɛɨɣ ɢ ɫ ɨɫɧɨɜɚɧɢɟɦ ɜ ɠɟɫɬɤɢɯ ɢ ɲɚɪɧɢɪɧɵɯ ɭɡɥɚɯ.
ɗɬɨ ɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɨɜ ɛɨɥɶɲɨɦ ɱɢɫɥɟ ɪɚɛɨɬ, ɧɚɩɪɢɦɟɪ [7, 10 – 13], ɝɞɟ ɩɨɤɚɡɚɧɨ, ɱɬɨ Ʉɗ ɦɨɝɭɬɩɪɟɞɫɬɚɜɥɹɬɶ ɫɨɛɨɣ ɤɚɤ ɫɢɫɬɟɦɭ ɧɟɫɤɨɥɶɤɢɯ ɫɨɟɞɢɧɟɧɧɵɯ ɞɪɭɝ ɫ ɞɪɭɝɨɦɫɬɟɪɠɧɟɣ, ɬɚɤ ɢ ɢɦɟɬɶ ɜɢɞ ɨɞɧɨɝɨ ɩɪɹɦɨɥɢɧɟɣɧɨɝɨ ɫɬɟɪɠɧɹ.ȼ ɞɚɧɧɨɦ ɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɩɪɢ ɪɚɫɱɟɬɟ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦ ɆɄɗɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɟɝɨ ɪɟɚɥɢɡɚɰɢɹ ɜ ɮɨɪɦɟ ɦɟɬɨɞɚ ɩɟɪɟɦɟɳɟɧɢɣ ɧɚ ɉɄ ɫɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ SCAD [19], ɜ ɤɨɬɨɪɨɣ ɢɫɩɨɥɶɡɭɸɬɫɹ ɬɨɥɶɤɨɩɪɹɦɨɥɢɧɟɣɧɵɟ ɫɬɟɪɠɧɟɜɵɟ ɷɥɟɦɟɧɬɵ.ȼ ɩɥɨɫɤɢɯ ɫɬɟɪɠɧɟɜɵɯ ɫɢɫɬɟɦɚɯ ɜ ɩɪɨɝɪɚɦɦɟ SCAD ɢɫɩɨɥɶɡɭɸɬɫɹɩɪɹɦɨɥɢɧɟɣɧɵɟ ɫɬɟɪɠɧɟɜɵɟ Ʉɗ ɞɜɭɯ ɬɢɩɨɜ:1. ɋɬɟɪɠɟɧɶ, ɪɚɛɨɬɚɸɳɢɣ ɬɨɥɶɤɨ ɜ ɭɫɥɨɜɢɹɯ ɩɪɨɞɨɥɶɧɵɯ ɞɟɮɨɪɦɚɰɢɣ. ȼɟɝɨ ɫɟɱɟɧɢɹɯ ɜɨɡɧɢɤɚɸɬ ɬɨɥɶɤɨ ɩɪɨɞɨɥɶɧɵɟ ɭɫɢɥɢɹ N .ȼ ɬɚɤɢɯ ɭɫɥɨɜɢɹɯ ɧɚɯɨɞɹɬɫɹ ɫɬɟɪɠɧɢ ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɮɟɪɦɵ, ɤɨɬɨɪɚɹɢɦɟɟɬ ɲɚɪɧɢɪɧɵɟ ɭɡɥɵ.
ɉɨɷɬɨɦɭ Ʉɗ ɬɢɩɚ 1 ɧɚɡɵɜɚɸɬ ɷɥɟɦɟɧɬɨɦ ɬɢɩɚ«ɫɬɟɪɠɟɧɶ ɩɥɨɫɤɨɣ ɮɟɪɦɵ».Ɉɞɧɚɤɨ ɬɚɤɨɣ ɷɥɟɦɟɧɬ (ɜɧɟɲɧɢɦ ɩɪɢɡɧɚɤɨɦ ɟɝɨ ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ ɹɜɥɹɟɬɫɹ ɧɚɥɢɱɢɟ ɲɚɪɧɢɪɨɜ ɩɨ ɟɝɨ ɤɨɧɰɚɦ ɢ ɨɬɫɭɬɫɬɜɢɟɩɨɩɟɪɟɱɧɨɣ ɧɚɝɪɭɡɤɢ ɧɚ ɧɟɝɨ) ɦɨɠɟɬ ɜɫɬɪɟɬɢɬɶɫɹ ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɆɄɗ ɢɲɚɪɧɢɪɧɨɣ ɛɚɥɤɢ ɢ ɪɚɦɵ.2. ɋɬɟɪɠɟɧɶ, ɜ ɫɟɱɟɧɢɹɯ ɤɨɬɨɪɨɝɨ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɦɨɝɭɬ ɜɨɡɧɢɤɧɭɬɶɢɡɝɢɛɧɵɟ, ɩɨɩɟɪɟɱɧɵɟ ɢ ɩɪɨɞɨɥɶɧɵɟ ɞɟɮɨɪɦɚɰɢɢ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɢɦɭɫɢɥɢɹ M , Q, N .ȼ ɬɚɤɢɯ ɭɫɥɨɜɢɹɯ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɪɚɛɨɬɚɸɬ ɫɬɟɪɠɧɢ ɩɥɨɫɤɨɣ ɪɚɦɵ.ɉɨɷɬɨɦɭ Ʉɗ ɬɢɩɚ 2 ɧɚɡɵɜɚɸɬ ɷɥɟɦɟɧɬɨɦ ɬɢɩɚ «ɫɬɟɪɠɟɧɶ ɩɥɨɫɤɨɣ ɪɚɦɵ».ɇɚ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɆɄɗ ɞɥɹ ɪɚɦ ɢ ɛɚɥɨɤ ɬɚɤɨɣ ɷɥɟɦɟɧɬ ɜɫɬɪɟɱɚɟɬɫɹ ɜɪɚɡɥɢɱɧɨɦ ɜɢɞɟ, ɤɨɬɨɪɵɣ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɱɢɫɥɨɦ ɜɧɭɬɪɟɧɧɢɯ ɫɜɹɡɟɣ,42ɩɪɢɤɪɟɩɥɹɸɳɢɯ ɟɝɨ ɤ ɧɚɦɟɱɟɧɧɵɦ ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɭɡɥɚɦ.
Ⱦɚɥɟɟ ɷɬɨɩɪɨɞɟɦɨɧɫɬɪɢɪɨɜɚɧɨ ɧɚ ɩɪɢɦɟɪɟ ɩɥɨɫɤɨɣ ɪɚɦɵ (ɪɢɫ. 3.1, ɚ), ɜɡɹɬɨɣ ɢɡ ɤɧɢɝɢ[19] ɚɜɬɨɪɨɜ ɜɵɱɢɫɥɢɬɟɥɶɧɨɝɨ ɤɨɦɩɥɟɤɫɚ SCAD. Ɋɚɦɚ ɝɟɨɦɟɬɪɢɱɟɫɤɢɧɟɢɡɦɟɧɹɟɦɚ ɢ ɨɞɢɧ ɪɚɡ ɫɬɚɬɢɱɟɫɤɢ ɧɟɨɩɪɟɞɟɥɢɦɚ ( n (nɨɩ 3nɤ ) (3 n1ɲ ) == (4 3 1) (3 3) 1 ) [1].ɛ)ɚ)6587(7)(6)(2)(8)(4)34(5)ZOY(1)ZX1(3)YX2Ɋɢɫ. 3.1ɉɪɢ ɩɨɫɬɪɨɟɧɢɢ ɚɥɝɨɪɢɬɦɚ ɆɄɗ ɜ ɩɪɨɝɪɚɦɦɟ SCAD ɫɬɟɪɠɧɟɜɚɹ ɫɢɫɬɟɦɚɫɨɨɬɧɨɫɢɬɫɹ ɫ ɩɪɚɜɨɣ ɞɟɤɚɪɬɨɜɨɣ ɫɢɫɬɟɦɨɣ ɤɨɨɪɞɢɧɚɬ XYZ (ɫɦ.
ɪɢɫ. 3.1, ɚ).Ɍɚɤɭɸ ɫɢɫɬɟɦɭ ɤɨɨɪɞɢɧɚɬ ɧɚɡɵɜɚɸɬ ɨɛɳɟɣ ɫɢɫɬɟɦɨɣ ɤɨɨɪɞɢɧɚɬ (ɈɋɄ) ɞɥɹ ɜɫɟɣɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ.ɉɥɨɫɤɚɹ ɫɬɟɪɠɧɟɜɚɹ ɫɢɫɬɟɦɚ ɫɱɢɬɚɟɬɫɹ ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɜ ɩɥɨɫɤɨɫɬɢXOZ (ɫɦ. ɪɢɫ. 3.1,ɚ).ȼ ɩɪɢɧɰɢɩɟ ɤɚɠɞɵɣ ɢɡ ɫɬɟɪɠɧɟɣ ɪɚɦɵ, ɩɪɢɜɟɞɟɧɧɨɣ ɧɚ ɪɢɫ. 3.1, ɚ, ɦɨɠɟɬɛɵɬɶ ɪɚɡɞɟɥɟɧ ɧɚ ɥɸɛɨɟ ɤɨɧɟɱɧɨɟ ɱɢɫɥɨ ɫɬɟɪɠɧɟɜɵɯ ɷɥɟɦɟɧɬɨɜ ɨɬɥɢɱɚɸɳɢɯɫɹɨɬ ɚɩɩɪɨɤɫɢɦɢɪɭɟɦɨɝɨ ɫɬɟɪɠɧɹ ɬɨɥɶɤɨ ɞɥɢɧɨɣ ɢ ɯɚɪɚɤɬɟɪɨɦ ɩɪɢɤɪɟɩɥɟɧɢɹɷɥɟɦɟɧɬɨɜ ɤ ɭɡɥɚɦ.ɉɨɷɬɨɦɭ ɩɪɢ ɩɨɫɬɪɨɟɧɢɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɆɄɗ ɧɟɨɛɯɨɞɢɦɨ, ɩɪɟɠɞɟɜɫɟɝɨ, ɜɵɛɪɚɬɶ ɪɚɰɢɨɧɚɥɶɧɨɟ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɱɢɫɥɨ ɤɨɧɟɱɧɵɯ ɫɬɟɪɠɧɟɜɵɯɷɥɟɦɟɧɬɨɜ, ɚɩɩɪɨɤɫɢɦɢɪɭɸɳɢɯ ɫɬɟɪɠɧɢ ɡɚɞɚɧɧɨɣ ɪɚɦɵ ɢ ɧɚɦɟɬɢɬɶ ɧɚ ɪɚɦɟɭɡɥɵ, ɜ ɤɨɬɨɪɵɯ Ʉɗ ɫɨɟɞɢɧɹɸɬɫɹ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɢ ɫ ɨɫɧɨɜɚɧɢɟɦ.ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɜɨɩɪɨɫɚ ɨ ɩɨɫɬɪɨɟɧɢɢ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɫɬɟɪɠɧɟɜɨɣ43ɫɢɫɬɟɦɵ ɞɥɹ ɟɟ ɪɚɫɱɟɬɚ ɆɄɗ ɧɚ ɩɟɪɫɨɧɚɥɶɧɨɦ ɤɨɦɩɶɸɬɟɪɟ ɫ ɩɨɦɨɳɶɸɩɪɨɝɪɚɦɦɵ SCAD ɛɭɞɟɦ ɭɱɢɬɵɜɚɬɶ ɫɥɟɞɭɸɳɟɟ (ɫɦ.
ɦɟɬɨɞɢɱɟɫɤɢɟ ɭɤɚɡɚɧɢɹ ɜɤɧɢɝɟ [19] ɢ ɜ ɫɩɪɚɜɤɟ ɤ ɩɪɨɝɪɚɦɦɟ).1. Ʉɨɧɟɱɧɵɟ ɷɥɟɦɟɧɬɵ ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɆɄɗ ɞɥɹ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵɫɱɢɬɚɸɬɫɹ ɫɨɟɞɢɧɟɧɧɵɦɢ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɢ ɫ ɨɫɧɨɜɚɧɢɟɦ ɜ ɧɚɦɟɱɟɧɧɵɯ ɧɚɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɭɡɥɚɯ.2. Ɂɚ ɨɫɧɨɜɧɵɟ ɧɟɢɡɜɟɫɬɧɵɟ ɜɟɥɢɱɢɧɵ, ɤɨɬɨɪɵɟ ɜ ɆɄɗ ɜ ɮɨɪɦɟɦɟɬɨɞɚ ɩɟɪɟɦɟɳɟɧɢɣ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜ ɩɟɪɜɭɸ ɨɱɟɪɟɞɶ, ɩɪɢɧɢɦɚɸɬɤɨɦɩɨɧɟɧɬɵ ɥɢɧɟɣɧɵɯ ɢ ɭɝɥɨɜɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɜɫɟɯ ɧɚɦɟɱɟɧɧɵɯ ɭɡɥɨɜɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɢɯ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ.3. ɉɨ ɧɚɣɞɟɧɧɵɦ ɩɟɪɟɦɟɳɟɧɢɹɦ ɭɡɥɨɜ ɤɚɠɞɨɝɨ ɤɨɧɟɱɧɨɝɨ ɷɥɟɦɟɧɬɚɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɭɫɢɥɢɹ ɜ ɫɜɹɡɹɯ, ɩɪɢɫɨɟɞɢɧɹɸɳɢɯɤɨɧɟɱɧɵɟ ɷɥɟɦɟɧɬɵ ɤ ɭɡɥɚɦ.Ʉɨɦɩɨɧɟɧɬɵ ɢɫɤɨɦɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɭɡɥɨɜ ɜ ɆɄɗ ɨɛɨɡɧɚɱɚɸɬɫɹ ɜɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɨɫɹɦɢ ɨɛɳɟɣ ɫɢɫɬɟɦɵuZ (3)u 2i3iɤɨɨɪɞɢɧɚɬ, ɤ ɤɨɬɨɪɨɣ ɨɬɧɨɫɢɬɫɹ ɪɚɫɱɟɬɧɚɹu 5iɫɯɟɦɚ.u 6iȼ ɩɪɨɝɪɚɦɦɟ SCAD, ɝɞɟ ɢɫɩɨɥɶɡɭɟɬɫɹu1iɩɪɚɜɚɹ ɫɢɫɬɟɦɚ ɨɫɟɣ ɤɨɨɪɞɢɧɚɬ XYZ (ɪɢɫ.i3.1), ɜ ɬɚɛɥɢɰɚɯ ɫ ɪɟɡɭɥɶɬɚɬɚɦɢ ɪɚɫɱɟɬɨɜu 4iY (2)ɤɨɦɩɨɧɟɧɬɵɩɟɪɟɦɟɳɟɧɢɣɥɸɛɨɝɨX (1)ɠɟɫɬɤɨɝɨ ɭɡɥɚ i ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɣOɨɛɨɡɧɚɱɚɸɬɫɹɫɬɟɪɠɧɟɜɨɣɫɢɫɬɟɦɵɫɨɨɬɜɟɬɫɬɜɟɧɧɨ Xi, Yi, Zi, UXi, UYi UZi.Ɋɢɫ.
3.2ɗɬɢɦ ɧɚɩɪɚɜɥɟɧɢɹɦ ɤɨɦɩɨɧɟɧɬɨɜɩɟɪɟɦɟɳɟɧɢɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɭɦɟɪɚɰɢɹ: 1, 2. 3, 4, 5, 6, ɢɫɩɨɥɶɡɨɜɚɧɧɚɹ ɩɪɢɨɛɨɡɧɚɱɟɧɢɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɤɨɦɩɨɧɟɧɬɨɜ ɩɟɪɟɦɟɳɟɧɢɣ ɧɚ ɪɢɫ 3.2).ɇɚ ɪɢɫ. 3.2 ɩɨɤɚɡɚɧɵ ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɧɚɩɪɚɜɥɟɧɢɹ ɤɨɦɩɨɧɟɧɬɨɜɩɟɪɟɦɟɳɟɧɢɣ, ɩɪɢɧɹɬɵɟ ɩɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɚɥɝɨɪɢɬɦɚ ɆɄɗ.Ⱦɥɹ ɩɥɨɫɤɨɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɧɚɯɨɞɹɳɟɣɫɹ ɜ ɩɥɨɫɤɨɫɬɢ XOZ,ɩɨɥɨɠɟɧɢɟ ɩɥɨɫɤɨɝɨ ɠɟɫɬɤɨɝɨ ɭɡɥɚ i ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨɦɩɨɧɟɧɬɚɦɢ ɥɢɧɟɣɧɵɯɩɟɪɟɦɟɳɟɧɢɣ Xi, Zi (ɢɥɢ u1i , u3i ) ɢ ɭɝɥɨɦ ɩɨɜɨɪɨɬɚ UYi (ɢɥɢ u5i ) ɜɨɤɪɭɝ ɨɫɢɩɚɪɚɥɥɟɥɶɧɨɣ ɨɫɢ Y (ɫɦ.
ɪɢɫ. 3.2).ɉɨɫɤɨɥɶɤɭ ɬɪɭɞɨɟɦɤɨɫɬɶ ɱɢɫɥɟɧɧɨɣ ɪɟɚɥɢɡɚɰɢɢ ɚɥɝɨɪɢɬɦɚ ɆɄɗ ɡɚɜɢɫɢɬɨɬ ɱɢɫɥɚ ɧɟɢɡɜɟɫɬɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɜɨ ɜɫɟɯ ɧɚɦɟɱɟɧɧɵɯ ɭɡɥɚɯ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɵ, ɠɟɥɚɬɟɥɶɧɨ ɧɚɦɟɱɚɬɶ ɧɚɢɦɟɧɶɲɟɟ ɱɢɫɥɨ ɭɡɥɨɜ, ɚ ɡɧɚɱɢɬɪɚɡɞɟɥɹɬɶ ɫɬɟɪɠɧɟɜɭɸ ɫɢɫɬɟɦɭ ɧɚ ɧɚɢɦɟɧɶɲɟɟ ɱɢɫɥɨ ɫɬɟɪɠɧɟɜɵɯ ɤɨɧɟɱɧɵɯ44ɷɥɟɦɟɧɬɨɜ.ɇɚɢɦɟɧɶɲɟɟ ɱɢɫɥɨ ɫɬɟɪɠɧɟɜɵɯ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɨɜ ɩɨɥɭɱɢɬɫɹ ɬɨɝɞɚ,ɤɨɝɞɚ ɭɡɥɵ ɜ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɆɄɗ ɧɚɡɧɚɱɟɧɵ ɜ ɡɚɞɚɧɧɨɣ ɫɬɟɪɠɧɟɜɨɣ ɫɢɫɬɟɦɟ ɜɭɡɥɚɯ (ɜ ɬɨɦ ɱɢɫɥɟ ɲɚɪɧɢɪɧɵɯ) ɫɨɟɞɢɧɟɧɢɹ ɩɪɹɦɵɯ ɫɬɟɪɠɧɟɣ ɦɟɠɞɭ ɫɨɛɨɣ ɢ ɫɨɫɧɨɜɚɧɢɟɦ, ɚ ɬɚɤɠɟ ɧɚ ɫɜɨɛɨɞɧɵɯ (ɤɨɧɫɨɥɶɧɵɯ) ɤɨɧɰɚɯ ɫɬɟɪɠɧɟɣ..Ɉɞɧɚɤɨ ɢɧɨɝɞɚ, ɧɚɩɪɢɦɟɪ, ɜ ɦɟɫɬɚɯ ɩɪɢɥɨɠɟɧɢɹ ɫɨɫɪɟɞɨɬɨɱɟɧɧɵɯ ɫɢɥ ɢɦɨɦɟɧɬɨɜ, ɢɥɢ ɜ ɞɪɭɝɢɯ ɫɟɱɟɧɢɹɯ ɫɬɟɪɠɧɟɣ ɫ ɰɟɥɶɸ ɩɨɥɭɱɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣɢɧɮɨɪɦɚɰɢɢ ɨ ɩɟɪɟɦɟɳɟɧɢɹɯ ɢ ɭɫɢɥɢɹɯ ɜ ɧɢɯ, ɩɪɢɯɨɞɢɬɫɹ ɧɚɡɧɚɱɚɬɶ ɜɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɱɢɫɥɨ ɭɡɥɨɜ.ɋ ɰɟɥɶɸ ɜɵɛɨɪɚ ɧɚɢɦɟɧɶɲɟɝɨ ɱɢɫɥɚ ɧɟɢɡɜɟɫɬɧɵɯ ɩɟɪɟɦɟɳɟɧɢɣ ɜɪɚɫɱɟɬɧɨɣ ɫɯɟɦɟ ɆɄɗ ɪɚɦɵ, ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ.
3.1, ɚ, ɩɪɢɦɟɦ ɜɚɪɢɚɧɬ ɟɟɪɚɡɛɢɟɧɢɹ ɧɚ ɦɢɧɢɦɚɥɶɧɨɟ ɱɢɫɥɨ ɫɬɟɪɠɧɟɜɵɯ Ʉɗ, ɤɨɝɞɚ ɤɚɠɞɵɣ ɫɬɟɪɠɟɧɶɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɤɚɤ ɨɞɢɧ Ʉɗ ɬɢɩɚ 2.ɉɪɨɞɟɦɨɧɫɬɪɢɪɭɟɦ ɨɫɨɛɟɧɧɨɫɬɢ ɩɪɨɰɟɞɭɪɵ ɩɨɫɬɪɨɟɧɢɹ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵɆɄɗ ɪɚɦɵ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɝɪɚɦɦɵ SCAD. ɉɪɢ ɷɬɨɦ ɛɭɞɟɦɪɭɤɨɜɨɞɫɬɜɨɜɚɬɶɫɹ ɭɤɚɡɚɧɢɹɦɢ ɚɜɬɨɪɨɜ ɜɵɱɢɫɥɢɬɟɥɶɧɨɝɨ ɤɨɦɩɥɟɤɫɚ SCAD,ɩɪɢɜɟɞɟɧɧɵɯ ɜ ɤɧɢɝɟ [19] ɢ ɫɩɪɚɜɤɟ ɤ ɩɪɨɝɪɚɦɦɟ, ɚ ɬɚɤɠɟ ɦɟɬɨɞɢɱɟɫɤɢɦɢɭɤɚɡɚɧɢɹɦɢ, ɞɚɧɧɵɦɢ ɜ ɧɚɫɬɨɹɳɟɦ ɩɨɫɨɛɢɢ.3.2. ɉɨɫɬɪɨɟɧɢɟ ɪɚɫɱɟɬɧɨɣ ɫɯɟɦɵ ɆɄɗ ɧɚ ɷɬɚɩɚɯ ɩɨɫɬɚɧɨɜɤɢ ɨɩɨɪɧɵɯɫɜɹɡɟɣ ɢ ɨɞɢɧɨɱɧɵɯ ɲɚɪɧɢɪɨɜ ɧɚ ɤɨɧɟɱɧɵɯ ɷɥɟɦɟɧɬɚɯɉɟɪɜɨɧɚɱɚɥɶɧɨ ɞɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɪɚɦɵ ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦɵ SCADɫɬɪɨɢɬɫɹ ɩɪɨɦɟɠɭɬɨɱɧɚɹ ɪɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɆɄɗ ɫ ɧɚɡɧɚɱɟɧɢɟɦ ɬɨɥɶɤɨ ɠɟɫɬɤɢɯɭɡɥɨɜ (ɪɢɫ.
