Динамика: упругопластический брус под медленным импульсом — остаточная деформация равна квазистатической разгрузке
Неявная переходная динамика / пластичностьPASS · 0.42%Стальной брус с J2-пластичностью и линейным изотропным упрочнением нагружен за предел текучести гладким импульсом sin² много длиннее его периодов и затем успокаивается при слабом демпфировании Рэлея. После затухания колебаний остаточное удлинение должно совпасть с квазистатическим результатом «нагрузка–разгрузка» на той же сетке и с замкнутой формулой ε_p = (σ_max − σ_y)(1/E_t − 1/E). История пластичности фиксируется на каждом принятом шаге по времени.Стальной брус с J2-пластичностью и линейным изотропным упрочнением нагружен за предел текучести гладким импульсом sin² много длиннее его периодов и затем успокаивается при слабом демпфировании Рэлея. После затухания колебаний остаточное удлинение должно совпас… показать полностью
- Допуск:
- 5%
Постановка задачи
- Геометрия
- Брус 100 × 10 × 10 мм, линейные тетраэдры, размер элемента 10 мм; плоскости симметрии на трёх гранях (одноосное напряжённое состояние).
- Материал
- Сталь: E = 210 ГПа, ν = 0.3, ρ = 7850 кг/м³, J2-пластичность, σ_y = 250 МПа, касательный модуль E_t = 4.2 ГПа.
- Граничные условия
- Давление на торце 300 МПа, умноженное на k(t) = sin²(πt/t_P), t_P = 300·T₁ (T₁ = 4L/c), затем 60·T₁ свободного затухания; Newmark β = 1/4, γ = 1/2, Δt = T₁/20, Рэлей a = 2ζω₁, ζ = 1 %, кинематика малых деформаций.
- Контрольная величина
- Остаточное перемещение торца после затухания против квазистатического пути λ: 1 → 0 на той же сетке и замкнутой формулы ε_p·L.
Терминал WebCAE
Вставьте команды в панель Terminal в WebCAE. Скрипт использует штатный текстовый DSL приложения; команды выполняются построчно:
units mm
material E=210e9 nu=0.3 density=7850 plasticity=j2 yield=250e6 hardening=linear et=4.2e9
primitive box dx=100 dy=10 dz=10
mesh tet size=10
fix surface number 1 component=x
fix surface number 3 component=y
fix surface number 5 component=z
load surface number 2 pressure=-300000000
solve transient dt=0.000003866830867 tend=0.02784118224 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rayleigh a=1624.892715 b=0 mass=consistent probes="100,5,5" outputs=500 frames=0
probe transient_displacement dir=x id="ures"
probe transient_peak dir=x id="upeak"
probe transient_steps id="steps"Сравнение результатов
| Эталонное значение | u_ост = 1.16667 мм (квазистатика)ε_p·L = 1.16667 мм |
| Результат WebCAE | u_ост = 1.17153 мм (динамика) |
| Погрешность | 0.42% |
| Допуск | 5% |
| Статус | PASS · 0.42% |
| Параметры сетки | брус 100×10×10 мм, тет4 размер 10 мм (72 тетр.); 7200 шагов (принято 7200, резок 0), 8009 итераций Ньютона (макс 2/шаг), 1621 факторизаций; ядро 1750 мс, скрипт 8.1 с на нативе |
Обновлено: 2026-10-22 · WebCAE solver